string url = "http://yourserver.com/endpoint";
byte[] body = Encoding.UTF8.GetBytes(json);    

Dictionary headers = new Dictionary();
headers.Add( "Content-Type", "application/json" );
headers.Add( "X-HTTP-Method-Override", "PUT" );
WWW www = new WWW(url, body, headers);

http://stackoverflow.com/questions/29668059/unity-use-http-put-in-unity3d