Someone told me it is now up to the mother of a child as to weather a father can give up his parental rights to a child in the state of Georgia, is this true? Are there any loopholes?

Well first a father can never just give up his rights unless the other parent agrees, and even if that other parent agrees then the judge will still have to OK it. ( and in GA most will not)

Also except for adoption of the child in GA if the father does get to give up their rights, they still have to pay child support.