Publishing User Scores
You can publish stories about a user�s score by issuing an HTTP POST to /USER_ID/scores and specifying a user�s score in the score parameter. An app access token (shown in the example above) is required to make this API call.
graph.facebook.com/USER_ID/scores
score=USER_SCORE&access_token=APP_ACCESS_TOKEN
Scores show up in the app ticker in various story types that help drive re-engagement back to your app:
More information in their blog post