Regulatory Improvement Act of 2013 - Establishes in the legislative branch the Regulatory Improvement Commission. Requires the Commission to evaluate and provide recommendations and proposed legislation for modification, consolidation, or repeal of regulations that have been finalized not later than 10 years before the establishment of the Commission and have not been amended after being finalized (covered regulations) for the purpose of reducing compliance costs, encouraging growth and innovation, improving competitiveness, and protecting public safety. Sets forth reporting requirements for the Commission and procedures for congressional consideration of Commission reports and recommendations and proposed legislation.