Future of Arms Control Act This bill restricts the United States from taking certain actions in the event that the President does not extend the Measures for the Further Reduction and Limitation of Strategic Offensive Arms (New START Treaty) by November 3, 2020. (The New START Treaty, a nuclear nonproliferation agreement between the United States and Russia, is set to expire in February 2021 but may be extended to February 2026.) If the treaty is not extended, the United States may not take any action that would violate the treaty until March 1, 2021, unless (1) the President certifies to Congress the intention to waive this restriction, and (2) Congress does not enact a joint resolution of disapproval within 15 days of the certification. The President's certification shall contain (1) a determination that Russia has materially violated the treaty and that this violation gravely threatens U.S. security, and (2) the reasoning behind this determination.