Albatross and Petrel Conservation Act This bill authorizes the United States Fish and Wildlife Service (USFWS) and the National Marine Fisheries Service (NMFS) to promulgate regulations to implement and enforce the Agreement on the Conservation of Albatrosses and Petrels, done at Cape Town, South Africa, on February 2, 2001. This bill authorizes USFWS and NMFS to take action to conserve albatrosses and petrels, including to: reestablish albatrosses and petrels; prevent the introduction of, eradicate, or control invasive and nonnative species that have or may have an adverse effect on albatrosses and petrels; conserve, protect, and restore breeding sites; undertake measures for the conservation and protection of albatross and petrel habitat and other marine habitats that provide food for albatrosses and petrels; undertake scientific research to assess the effects of pollutants and marine debris on albatrosses and petrels; develop and implement measures to prevent, minimize, or mitigate the taking or disturbance of albatrosses and petrels in U.S. waters or by U.S. vessels; develop and undertake measures to minimize the bycatch of albatrosses and petrels; and share information on the conservation status of albatrosses and petrels, the threats facing albatrosses and petrels, and any actions taken under this bill. This bill prohibits the taking of an albatross or petrel without a permit, authorization, or exemption. USFWS, in consultation with NMFS, may authorize the taking of an albatross or petrel under exceptional circumstances or incidental to otherwise lawful activities. This bill gives the USFWS, the NMFS, and the Coast Guard authority to enforce this bill. This bill authorizes cooperation with other countries to achieve and maintain a favorable conservation status of albatrosses and petrels.