Stop Arming Human Rights Abusers Act This bill requires the President to impose certain sanctions on foreign governments that have engaged in genocide, crimes against humanity, or war crimes. Upon determining that the government of a foreign country has committed such crimes, the President must sanction the country by prohibiting (1) any U.S. security assistance; and (2) arms sales, including the sale, transfer, delivery, and export licensing of defense articles and defense services. Additionally, the bill prohibits federal, state, and local law enforcement agencies from participating in any exchange with the police, military, or security forces of the sanctioned country. The bill establishes the U.S. Commission on Atrocity Accountability and Human Rights to review violations of international human rights law or international humanitarian law and to make policy recommendations with respect to the imposition and termination of sanctions specified in the bill.