Me and my exgirlfriend is having a baby, She does not want the baby but I do we live in Georgia can she sign her parental rights over to me..

No, but she can cede custody to you. As soon as the child is born, file for full legal and physical custody. If she raises no objections, there should be no problem. However, this will not be permanent. If she changes her mind at sometime in the future, she can go to court and ask for visitation and partial custody. If she agrees to cede custody to you, its unlikely the court will switch custody, but they will allow her partial custody.

The only way you will terminate her rights is if you marry and she agrees to let your wife adopt the child.