Use implicit OAuth flow. Load the specified URL with necessary query parameters into a webview and when authentication is done you can get the access_token from the redirect_uri. You can have the webview handle the redirect_uri by setting a custom webview client.
Example:
private class ExampleWebViewClient extends WebViewClient
{
@Override
public boolean shouldOverrideUrlLoading(WebView view, String url)
{
if (url.startsWith(MY_REDIRECT_URI))
{
//parse the URL here to get the access_token
return true;
}
return false;
}
}
And while initializing the webview, do
webview.setWebViewClient(new ExampleWebViewClient());