If my child's father signs an Acknowledgement of Paternity, can he sign away his legal rights?

I am pregnant, and my child's father wants nothing to do with the child, other than what he is legally obligated to do. I am not interested in dealing with him any further, and would like to terminate his rights. If he is willing, can he sign an acknowledgement of paternity and then terminate his rights voluntarily? My current boyfriend would like to eventually adopt my child, once we are married and this would make it the easiest.