how to add friends on game center without using phone contact

Bulldog_15,

I'm glad you decided to reach out on the Apple Support Communities. If I understand correctly, you’re wanting to add a friend without having them in your Contacts. Do you know their telephone number? If so, you can invite them by entering their phone number as well. They’ll receive an invitation in Messages.

This article explains:

Use Game Center to play with friends - Apple Support

Take care.