Is there a way to get someone to sign over there rights without a DNA test?

If you have not already done so, you probably want to contact your local Juvenile and Domestic Relations District Court to file a Petition for Custody.  Once you have a custody order in place, you can allow the father to visit the child without worrying that he will keep her.  If he did so, he would be in violation of the court order and you would have the full force of the law behind you to retrieve your child.  There is no procedure by which he can "sign over his rights" to the child.  He could sign an agreed order for custody, but that's about it.  Termination of parental rights is a long and complicated procedure that is only done in cases of severe abuse or neglect.  Usually, every other alternative is exhausted before a court would terminate someone's parental rights.  As far as the DNA test, he is entitled to this if you are seeking child support from him and he disputes paternity. This answer is given in accordance with the laws of Virginia and may not be applicable in any other state.  It should not be construed as legal advice, as that would require a more thorough analysis of all of the facts involved in a specific case.