It looks like there are a lot of Facebook users on Codeforces. But they could not easily authorize with their Facebook account until now. Well, now they can!
You can connect your Codeforces account with your Facebook account on profile settings page:
Just click the connect/update button, allow Codeforces to have access and save settings.
Besides that method, you can also connect your accounts while authorizing — if your Facebook account is not yet connected, you will be asked to either create a new account or to connect it with existing one.
To connect with an existing account you will need to log in using already known method.