Robert Levinson Hostage Recovery and Hostage-Taking Accountability Act This bill establishes various entities and procedures to address the wrongful detainment of U.S. nationals abroad. The President shall appoint a Special Presidential Envoy for Hostage Affairs. The envoy's duties shall include leading diplomatic engagement on U.S. hostage policy and coordinating diplomatic engagements in support of hostage recovery efforts. The President shall establish an interagency Hostage Recovery Fusion Cell, which shall assess and track all hostage cases of U.S. nationals and coordinate agency efforts to safely recover hostages. The President shall also establish the Hostage Recovery Group, which shall make recommendations regarding hostage recovery options and coordinate the development and implementation of U.S. hostage recovery policies. The President is authorized to impose visa- and property-blocking sanctions against any foreign person responsible for or complicit in the unlawful or wrongful detention of a U.S. national abroad. The Department of State shall review cases where U.S. nationals are detained abroad and refer instances of wrongful or unlawful detainment to the Special Presidential Envoy for Hostage Affairs.