Israeli Annexation Non-Recognition Act This bill prohibits a federal department or agency from recognizing, or implying recognition of, any claim by Israel of sovereignty over any part of the occupied West Bank in violation of international humanitarian law or customary international law. Further, it prohibits the use of certain federal funds to support specified activities in West Bank territory that has been unilaterally annexed by Israel or to facilitate or support such annexation. The Department of State must make an annual certification regarding any obligation or expenditure of such funds to Israel for these purposes.