Stop Arming Human Rights Abusers Act This bill imposes certain sanctions on countries that violate international human rights law or international humanitarian law. Specifically, the bill prohibits the provision of security assistance to, the sale or commercial export of arms to, or the exchange of law enforcement with a foreign country that has committed genocide, crimes against humanity, or war crimes. The bill also establishes the U.S. Commission on Atrocity Accountability and Human Rights to review such violations of international human rights law or international humanitarian law and to make policy recommendations with respect to the imposition of sanctions for such violations.