Do you mean this:
http://www.vbulletin.org/forum/showthread.php?t=173698 ? If so that's an insite auth API. What would be needed is an offsite auth api.
For example on this site:
http://stackoverflow.com/users/login you can login/register with your google account. If you say use google, they are sending a request to google (oauth 2.0 protocol I believe), you login via google, then google sends a request back to the site with your credentials (and various security tokens to confirm no funny business is going on), and you're logged in. You generally don't even have to enter username/password nonsense since you might already be logged in google, so as far as you're concerned you pressed a google button and you're logged in on the account associated with your gmail address.
Integrating such a feature is fairly easy these days thanks to things like:
http://hybridauth.sourceforge.net/ making a server for it though is a little more technical, you can find some server libraries here:
http://oauth.net/2/