Rules Review Act of 1981 - Requires the head of each Federal agency to publish in the Federal Register and submit to each House of Congress a copy and explanation of each proposed final rule. Declares that such a rule may become effective: (1) after 30 days of continuous session of Congress unless a petition calling for a review of the rule by the Senate or House is signed by 20 Senators and 87 Members of the House and filed in the appropriate House; and (2) 60 days after such a petition is filed unless Congress adopts a concurrent resolution disapproving the rule.

Sets forth procedures whereby the President may exempt from such requirements rules dealing with foreign policy, national defense, or emergency circumstances. Terminates any such exempted rule if a petition for review of the rule is filed in either House and Congress adopts a resolution of disapproval within a specified period after the rule becomes effective.

Sets forth House and Senate procedures for the review of a rule and the consideration of a resolution of disapproval.