<uses-permission android:name="android.permission.Camera" />

string[] PermissionsCamera =
    {
                  Manifest.Permission.Camera

        };
             int RequestId = 0;
            if (this.CheckSelfPermission(PermissionsCamera[0]) == (int)Permission.Granted)
            {
                // permission already granted

            }

            else
            {
                // request permissions
                Activity.RequestPermissions(PermissionsCamera, RequestId);
            }
        }

public override  void OnRequestPermissionsResult(int requestCode, string[] permissions, Permission[] grantResults)
        {
            switch (requestCode)
            {
                case RequestId:
                    {
                        if (grantResults[0] == Permission.Granted)
                        {
                            //Permission granted

                        }
                        else
                        {
                            //Permission Denied :

                        }
                    }
                    break;
            }
        }