Rare Earth Magnet Manufacturing Production Tax Credit Act of 2021 This bill allows a new tax credit for the domestic production of rare earth magnets manufactured in the ordinary course of a taxpayer's trade or business. The bill defines rare earth magnet as a permanent magnet comprised of (1) an alloy of neodymium, praseodymium, iron, boron, terbium, or dysprosium; or (2) an alloy of samarium, gadolinium, and cobalt.