I think Google Sign-In is only available for web pages (via JavaScript), IOS, and Android.
However,
OAuth2 works well on the Roku for letting users sign in with their Google accounts. For an example of an OAuth2 implementation for the Roku, check out the
Picasa2 Channel on GitHub:
https://github.com/belltown/Roku-Picasa2, in particular the files
private-git.brs (for instructions on how to set up your Google account keys),
oauth.brs (for the OAuth2 code) and
regScreen.brs (for the Registration Screen code).
https://github.com/belltown/