deploy.json

{
    "$schema": "https://schema.management.azure.com/schemas/2015-01-01/deploymentTemplate.json#",
    "contentVersion": "1.0.0.0",
    "parameters": {
        "functionAppName": {
            "type": "string",
            "metadata": {
                "description": "The name of the function app that you wish to create."
            }
        },
        "sku": {
            "type": "string",
            "allowedValues": [
                "Free",
                "Shared",
                "Basic",
                "Standard"
            ],
            "defaultValue": "Standard",
            "metadata": {
                "description": "The pricing tier for the hosting plan."
            }
        },
        "workerSize": {
            "type": "string",
            "allowedValues": [
                "0",
                "1",
                "2"
            ],
            "defaultValue": "0",
            "metadata": {
                "description": "The instance size of the hosting plan (small, medium, or large)."
            }
        },
        "storageAccountType": {
            "type": "string",
            "defaultValue": "Standard_LRS",
            "allowedValues": [
                "Standard_LRS",
                "Standard_GRS",
                "Standard_RAGRS"
            ],
            "metadata": {
                "description": "Storage Account type"
            }
        },
        "location": {
            "type": "string",
            "defaultValue": "[resourceGroup().location]",
            "metadata": {
                "description": "Location for all resources."
            }
        },
        "functionName":{
            "type":"string"
        },
        "functionFile": {
            "type": "string",
            "metadata": {
                "description": "The name of the function app that you wish to create."
            }
        }, 
        "proxiesFile": {
            "type": "string",
            "metadata": {
                "description": "The name of the function app that you wish to create."
            }
        },
        "functionSchedule": {
            "type":"string" ,
            "defaultValue": "0 15 0 0 0"           
        }             
    },
    "variables": {
        "functionName":"[parameters('functionName')]",
        "functionsAppName": "[parameters('functionAppName')]",
        "functionSchedule":"[parameters('functionSchedule')]",
        "hostingPlanName": "[parameters('functionAppName')]",
        "functionFile": "[parameters('functionFile')]",
        "proxiesFile": "[parameters('proxiesFile')]",        
        "storageAccountName": "[concat(uniquestring(resourceGroup().id), 'functions')]"
    },
    "resources": [
        {
            "type": "Microsoft.Storage/storageAccounts",
            "name": "[variables('storageAccountName')]",
            "apiVersion": "2016-12-01",
            "location": "[parameters('location')]",
            "kind": "Storage",
            "sku": {
                "name": "[parameters('storageAccountType')]"
            }
        },
        {
            "type": "Microsoft.Web/serverfarms",
            "apiVersion": "2015-04-01",
            "name": "[variables('hostingPlanName')]",
            "location": "[parameters('location')]",
            "properties": {
                "name": "[variables('hostingPlanName')]",
                "sku": "[parameters('sku')]",
                "workerSize": "[parameters('workerSize')]",
                "hostingEnvironment": "",
                "numberOfWorkers": 1
            }
        },
        {
            "name": "[concat(variables('functionsAppName'), '/', variables('functionName'))]",
            "type": "Microsoft.Web/sites/functions",
            "apiVersion": "2015-08-01",
            "properties": {
                "config": {
                    "bindings": [
                        {
                            "name": "myTimer",
                            "type": "timerTrigger",
                            "direction": "in",
                            "schedule": "[variables('functionSchedule')]"
                        }
                    ],
                    "disabled": false
                },
                "files": {
                    "run.csx": "[variables('functionFile')]",
                    "proxies.json": "[variables('proxiesFile')]"
                }
            },
            "dependsOn": [
                "[resourceId('Microsoft.Web/sites', variables('functionsAppName'))]"
            ]
        },        
        {
            "apiVersion": "2015-04-01",
            "type": "Microsoft.Web/sites",
            "name": "[variables('functionsAppName')]",
            "location": "[parameters('location')]",
            "kind": "functionapp",
            "properties": {
                "name": "[variables('functionsAppName')]",
                "serverFarmId": "[resourceId('Microsoft.Web/serverfarms', variables('hostingPlanName'))]",
                "hostingEnvironment": "",
                "clientAffinityEnabled": false,
                "siteConfig": {
                    "alwaysOn": true
                }
            },
            "dependsOn": [
                "[resourceId('Microsoft.Web/serverfarms', variables('hostingPlanName'))]",
                "[resourceId('Microsoft.Storage/storageAccounts', variables('storageAccountName'))]"
            ],
            "resources": [
                {
                    "apiVersion": "2016-03-01",
                    "name": "appsettings",
                    "type": "config",
                    "dependsOn": [
                        "[resourceId('Microsoft.Web/sites', variables('functionsAppName'))]",
                        "[resourceId('Microsoft.Storage/storageAccounts', variables('storageAccountName'))]"
                    ],
                    "properties": {
                        "AzureWebJobsStorage": "[concat('DefaultEndpointsProtocol=https;AccountName=',variables('storageAccountName'),';AccountKey=',listkeys(resourceId('Microsoft.Storage/storageAccounts', variables('storageAccountName')), '2015-05-01-preview').key1,';')]",
                        "AzureWebJobsDashboard": "[concat('DefaultEndpointsProtocol=https;AccountName=',variables('storageAccountName'),';AccountKey=',listkeys(resourceId('Microsoft.Storage/storageAccounts', variables('storageAccountName')), '2015-05-01-preview').key1,';')]",
                        "FUNCTIONS_EXTENSION_VERSION": "~1"
                    }
                }
            ]
        }
    ]
}

gistfile1.txt

there is no way to add proxies to a function app other than deploying the proxies.json file, here is the trick, first, you prepare a template for the function, a simple one, and add the proxies.json file to the list of files, let's take a look at the parameters and variables portion of the deploy.json file: 

    "parameters": {
        "functionAppName": {
            "type": "string",
            "metadata": {
                "description": "The name of the function app that you wish to create."
            },
        "functionName":{
            "type":"string"
        },
        "functionFile": {
            "type": "string"
        }, 
        "proxiesFile": {
            "type": "string"
        }              
    },
    "variables": {
        "functionName":"[parameters('functionName')]",
        "functionsAppName": "[parameters('functionAppName')]",
        "functionFile": "[parameters('functionFile')]",
        "proxiesFile": "[parameters('proxiesFile')]",        
        "storageAccountName": "[concat(uniquestring(resourceGroup().id), 'functions')]"
    },
we declare input parameters that we can use in our template as variables, and the in the function resource declaration we use our variables:

        {
            "name": "[concat(variables('functionsAppName'), '/', variables('functionName'))]",
            "type": "Microsoft.Web/sites/functions",
            "apiVersion": "2015-08-01",
            "properties": {
                "config": {
                    "bindings": [
                        {
                            "name": "myTimer",
                            "type": "timerTrigger",
                            "direction": "in",
                            "schedule": "[variables('functionSchedule')]"
                        }
                    ],
                    "disabled": false
                },
                "files": {
                    "run.csx": "[variables('functionFile')]",
                    "proxies.json": "[variables('proxiesFile')]"
                }
            },
            "dependsOn": [
                "[resourceId('Microsoft.Web/sites', variables('functionsAppName'))]"
            ]
        },  
to get the content of our files and pass it as parameters we can use for example Powershell to read each file's contents:

# Read the contents of the function file and assemble deployment parameters
$ProxiesFilePath="./proxies.json"
$proxiesFileContents = [System.IO.File]::ReadAllText($ProxiesFilePath)

$FunctionFilePath="./run.csx"
$functionFileContents = [System.IO.File]::ReadAllText($FunctionFilePath)

$templateParameters = @{}

$templateParameters.Add("functionFile", $functionFileContents)
$templateParameters.Add("proxiesFile", $proxiesFileContents)
and then we use Azure CLI or PowerShell to deploy our function:

az group deployment create \
   --name testFunctionDeployment \
   --resource-group msdn-demos-resources \
   --template-file deploy.json \
   --parameters functionFile=$templateParameters.functionFile proxiesFile=$templateParameters.proxiesFile functionName="myFunc"

proxies.json

{
    "$schema": "http://json.schemastore.org/proxies",
    "proxies": {
        "proxyHomePage": {
        "matchCondition": {
            "methods": [ "GET" ],
            "route": "/"
        },
        "backendUri": "%WEB_HOST%/index.html"
        },
        "proxyImages": {
        "matchCondition": {
            "methods": [ "GET" ],
            "route": "/images/{*restOfPath}"
        },
        "backendUri": "%WEB_HOST%/images/{restOfPath}"
        }
    }
}

run.csx

#r "Newtonsoft.Json"

using System.Net;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Extensions.Primitives;
using Newtonsoft.Json;

public static async Task<IActionResult> Run(HttpRequest req, ILogger log)
{
    log.LogInformation("C# HTTP trigger function processed a request.");

    string name = req.Query["name"];

    string requestBody = await new StreamReader(req.Body).ReadToEndAsync();
    dynamic data = JsonConvert.DeserializeObject(requestBody);
    name = name ?? data?.name;

    return name != null
        ? (ActionResult)new OkObjectResult($"Hello, {name}")
        : new BadRequestObjectResult("Please pass a name on the query string or in the request body");
}

test.ps1

# Read the contents of the function file and assemble deployment parameters
$ProxiesFilePath="./proxies.json"
$proxiesFileContents = [System.IO.File]::ReadAllText($ProxiesFilePath)

$FunctionFilePath="./run.csx"
$functionFileContents = [System.IO.File]::ReadAllText($FunctionFilePath)

$templateParameters = @{}

$templateParameters.Add("functionFile", $functionFileContents)
$templateParameters.Add("proxiesFile", $proxiesFileContents)

az group deployment create `
   --name testFunctionDeployment `
   --resource-group msdn-demos-resources `
   --template-file deploy.json `
   --parameters functionFile=$templateParameters.functionFile proxiesFile=$templateParameters.proxiesFile functionName="myFunc"