Unnecessary Agency Regulations Reduction Act of 2021 This bill requires the Office of Information and Regulatory Affairs to annually report a list of major rules (i.e., rules with a significant economic impact, cost to consumers, or adverse effects on competition) that it recommends should be consolidated or repealed because they are outdated, duplicative, or incur excessive compliance costs. Congress must review the list to determine, and recommend by joint resolution, any such rules to consolidate or repeal.