Rare Earth Magnet Manufacturing Production Tax Credit Act of 2022 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, iron, and boron, which may also include praseodymium, terbium, or dysprosium; or (2) an alloy of samarium and cobalt, which may also include gadolinium or any associated host mineral of a component rare earth material.