Cuban Family Reunification Parole Act of 2022 This bill directs the Department of State to restart processing applications under the Cuban Family Reunification Parole Program. (The program, which was suspended in 2017, allows eligible U.S. citizens and lawful permanent residents to apply for parole for family members in Cuba, who can then enter the United States while waiting for immigrant visas.) The State Department must prioritize applications filed before this bill's enactment and ensure that the adjudication of such applications begin no later than six months after this bill's enactment date.