Securing American Acquisitions, Readiness, and Military Stockpiles Act of 2022 or the Securing American ARMS Act of 2022 This bill provides that acquisition procedures other than competitive procedures may be used to (1) replenish United States stockpiles with like defense articles when stockpiles are diminished as a result of the response to an armed attack by a foreign adversary against a U.S. ally or partner, or (2) contract for the movement or delivery of defense articles transferred to such ally or partner through the President's drawdown authorities in connection with such response, provided that the United States is not a party to the hostilities. The head of the applicable agency must provide the congressional defense committees written notification of the use of such procedures within one week after such use.