In my android application, user can logging in using facebook/twitter.
https://graph.facebook.com/username/picture
https://api.twitter.com/1/users/profile_imag
Use an AsyncTask to download it and save it to your app's disk space. In your database, just store the file path of the picture (I would save it with the filename being the FB user id).
You can see how to use an AsyncTask to do a web connection in my code at github. https://github.com/nedwidek/Android-Rest-API
I'd need to switch workspaces to get to code that works with the local storage.