It's not only possible, but it's done that way!
Open a WebView, redirect the user to the authentication URL of your social network, and when the user navigates back after authentication, grab the token from the URL, close the WebView, and proceed with calling the API of the social network.
All social network SDKs, such as the Facebook SDK, work that way. If you want to look at how it's done, you can look at the classes of http://code.google.com/p/socialauth-android. It's an open source project that I am part of.