Well, you donβt say if you are platform specific. And there are many third-party authorization options.
But I can offer two solutions (true, my own code, etc.), both of them use PhoneGap for Android and PhoneGap plugins. The key code element for me was the onLocationChange callback function of the ChildBrowser plugin. Your application can take the user to other sites for authorization or something else, but still get control back.
Tutorial on using the Twitter REST API (OAuth 1, ChildBrowser, jsOAuth plugin)
Free Android app + Source on github : AppLaud App (OpenID, ChildBrowser, custom server)
source share