Migratory Bird Treaty Amendment Act of 2013 - Amends the Migratory Bird Treaty Act to allow an agricultural producer, or a hunter with the producer's permission, to take migratory game birds by the aid of baiting, if: (1) the manipulation occurs on the producer's land on which a crop was not harvestable during the current or immediately preceding crop year due to a natural disaster, and (2) a local representative of the Secretary of Agriculture (USDA) confirms that the crop has been destroyed and that it would not be economically practicable to harvest the crop.