Special Immigrant Visas for Afghan Fulbright Scholars Act of 2021 This bill authorizes special immigrant visas for qualifying citizens or nationals of Afghanistan who were selected for certain educational and cultural exchange programs. Specifically, a citizen or national of Afghanistan (and any accompanying spouse or child of such an individual) may be eligible for a special immigrant visa if the individual was selected on or after October 7, 2001, to participate in a qualifying educational or cultural exchange program administered by the Department of State, including the J. William Fulbright Educational Exchange Program.