According to the article Raped, pregnant and ordeal not over,So, should male rapists have custody and visitations rights to the children they father?...in the vast majority of states -- 31 -- men who father through rape are able to assert the same custody and visitation rights to their children that other fathers enjoy. When no law prohibits a rapist from exercising these rights, a woman may feel forced to bargain away her legal rights to a criminal trial in exchange for the rapist dropping the bid to have access to her child.
When faced with the choice between a lifetime tethered to her rapist or meaningful legal redress, the answer may be easy, but it is not painless. For the sake of her child, the woman will sacrifice her need to see her once immensely powerful perpetrator humbled by the court.
I know it because I lived it. I went to law school to learn how to stop it.