To enable CORS support in django-tastypie, use the following code snipet. Then create your tastypie resources as a subclass of BaseCorsResource.Basic code courtesy Daniel Conzalez of http://codeispoetry.me/index.php/make-your-django-tastypie-api-cross-domain/.I added documentation and the post_list method.

cors.py

'''
Add CORS headers for tastypie APIs

Usage:
   class MyModelResource(CORSModelResource):
       ...
       
   class MyResource(CORSResource):
       ...
       
Authors:
   original source by http://codeispoetry.me/index.php/make-your-django-tastypie-api-cross-domain/
   extensions by @miraculixx
   * deal with ?format requests
   * always return CORS headers, even if always_return_data is False
   * handle exceptions properly (e.g. raise tastypie.BadRequests) 
   * provide two distinct classes for ModelResource and Resource classes
'''
from django.http.response import HttpResponse
from tastypie import http
from tastypie.exceptions import ImmediateHttpResponse
from tastypie.resources import csrf_exempt
from tastypie.resources import Resource, ModelResource
import logging

class BaseCorsResource(Resource):
    """
    Class implementing CORS
    """
    def error_response(self, *args, **kwargs):
        response = super(BaseCorsResource, self).error_response(*args, **kwargs)
        return self.add_cors_headers(response, expose_headers=True)
        
    def add_cors_headers(self, response, expose_headers=False):
        response['Access-Control-Allow-Origin'] = '*'
        response['Access-Control-Allow-Headers'] = 'content-type, authorization'
        if expose_headers:
            response['Access-Control-Expose-Headers'] = 'Location'
        return response    
    
    def create_response(self, *args, **kwargs):
        """
        Create the response for a resource. Note this will only
        be called on a GET, POST, PUT request if 
        always_return_data is True
        """
        response = super(BaseCorsResource, self).create_response(*args, **kwargs)
        return self.add_cors_headers(response)

    def post_list(self, request, **kwargs):
        """
        In case of POST make sure we return the Access-Control-Allow Origin
        regardless of returning data
        """
        #logger.debug("post list %s\n%s" % (request, kwargs));
        response = super(BaseCorsResource, self).post_list(request, **kwargs)
        return self.add_cors_headers(response, True)
    
    def post_detail(self, request, **kwargs):
        """
        In case of POST make sure we return the Access-Control-Allow Origin
        regardless of returning data
        """
        #logger.debug("post detail %s\n%s" (request, **kwargs));
        response = super(BaseCorsResource, self).post_list(request, **kwargs)
        return self.add_cors_headers(response, True)
    
    def put_list(self, request, **kwargs):
        """
        In case of PUT make sure we return the Access-Control-Allow Origin
        regardless of returning data
        """
        response = super(BaseCorsResource, self).put_list(request, **kwargs)
        return self.add_cors_headers(response, True)    
    
    def put_detail(self, request, **kwargs):
        response = super(BaseCorsResource, self).put_detail(request, **kwargs)
        return self.add_cors_headers(response, True)
        
    def method_check(self, request, allowed=None):
        """
        Check for an OPTIONS request. If so return the Allow- headers
        """
        if allowed is None:
            allowed = []
            
        request_method = request.method.lower()
        allows = ','.join(map(lambda s: s.upper(), allowed))

        if request_method == 'options':
            response = HttpResponse(allows)
            response['Access-Control-Allow-Origin'] = '*'
            response['Access-Control-Allow-Headers'] = 'Content-Type, Authorization'
            response['Access-Control-Allow-Methods'] = "GET, PUT, POST, PATCH"
            response['Allow'] = allows
            raise ImmediateHttpResponse(response=response)

        if not request_method in allowed:
            response = http.HttpMethodNotAllowed(allows)
            response['Allow'] = allows
            raise ImmediateHttpResponse(response=response)

        return request_method
    
    def wrap_view(self, view):
        @csrf_exempt
        def wrapper(request, *args, **kwargs):
            request.format = kwargs.pop('format', None)
            wrapped_view = super(BaseCorsResource, self).wrap_view(view)
            return wrapped_view(request, *args, **kwargs)
        return wrapper

#Base Extended Abstract Model
class CORSModelResource(BaseCorsResource, ModelResource):
    pass

class CORSResource(BaseCorsResource, Resource):
    pass

For the CORS:
pip install django-cors-headers
Go to django settings.py and then follow the given steps:
INSTALLED_APPS = (
...
'corsheaders',
...
)
MIDDLEWARE = [ # Or MIDDLEWARE_CLASSES on Django < 1.10
...
'corsheaders.middleware.CorsMiddleware',

...

]

CORS_ORIGIN_ALLOW_ALL = True

Thats done for CROS!!!!#