In the command line:
$ curl -X POST -u username:password -d '<build><buildType id="<build type id in teamcity>"/><comment><text>Build was triggered by curl.</text></comment><properties><property name="<parameter name>" value="<parameter value>"/></properties></build>' http://<teamcity host>/httpAuth/app/rest/buildQueue --header "Content-Type: application/xml" -H "Accept: application/json"
It should return JSON response. State field should have queued value.