Rape Survivor Child Custody Act - Directs the Attorney General to make grants to states that have in place a law that allows the mother of any child that was conceived through rape to seek court-ordered termination of the parental rights of her rapist with regard to that child, which the court shall grant upon clear and convincing evidence of rape.

Limits such a grant to: (1) an amount that is not greater than 10% of the average of the total funding of the 3 most recent awards a state received under the STOP Violence Against Women Formula Grant Program and the Sexual Assault Services Program; and (2) a 1-year term, subject to renewal for not more than 3 additional years.

Requires a state that receives such a grant to use: (1) 25% of grant funds for permissible uses under the STOP Violence Against Women Formula Grant Program, and (2) 75% of funds for permissible uses under the Sexual Assault Services Program.