This app shows how you can use the AJAX-like system in Shiny to authorize a user using Facebook's JavaScript library and pass the user's information to R for processing. Because of Facebook's app settings, in order for the app to work properly locally, you need to replace 127.0.0.1 in the URL with fuf.me (testing FB apps locally is a big pain and is out of the scope of this example, you might have to do lots of Googling and StackOverflow-ing to get it right).
Note that this example uses the AJAX system shown in another example.