Can a Father in the state of Georgia petition to relinquish his parental rights voluntarily and is a lawyer needed?

Yes he can, lawyer helps, but why? You want to give up rights to visit, give up rights to have a say about the child's health care. You don't have to do any of that if you don't want to. So just don't, they can't force you to use a single right you have.

I will assume you may be referring to the obligation of paying child support, that has nothing to do with your rights and you will have to always pay child support