Cut Red Tape Act of 2022 This bill establishes in the legislative branch the Regulatory Improvement Commission to make recommendations and propose legislation for modification, consolidation, or repeal of regulations that have been finalized not later than 10 years before the establishment of the commission for the purpose of reducing compliance costs, encouraging growth and innovation, improving competitiveness, and protecting public safety. The commission must give priority to such regulations that (1) impose disproportionately high costs on a small entity, (2) create substantial recurring paperwork burdens or transaction costs, or (3) could be made more effective while reducing regulatory costs. The bill sets forth reporting requirements for the commission and procedures for congressional consideration of commission reports, recommendations, and proposed legislation.