No Support for Terror Act This bill establishes measures to prevent the allocation or use of certain funds to support genocide or terrorism. Specifically, the bill requires the Department of the Treasury to instruct the U.S. Executive Director at the International Monetary Fund (IMF) to oppose the allocation of Special Drawing Rights (a currency support tool) to any country that is a perpetrator of genocide or a state sponsor of terrorism and to advocate that the IMF adopt a rule prohibiting such allocation. Further, the bill requires Treasury, the Department of State, and the U.S. Agency for International Development to jointly review and report on assistance provided to nongovernmental organizations and international organization to ensure such assistance is not being provided to the Taliban or other terrorist organizations. Each prime awardee of this assistance must provide evidence that all subawardees are complying with U.S. anti-terrorism financing laws.