To log in with Game Center you will need to connect your iOS device to your Game Center account.
Do so by accessing your device's Settings > Game Center. Ensure Game Center is turned on, and that you are connected to the correct Game Center Profile.
Do so by accessing your device's Settings > Game Center. Ensure Game Center is turned on, and that you are connected to the correct Game Center Profile.
If you want to sign into a different profile, tap "Use different Apple ID for Game Center" option located at the bottom of the Game Center Settings menu.