Protecting American Intellectual Property Act of 2022 This bill imposes sanctions on certain foreign individuals and entities involved in the theft of trade secrets belonging to a U.S. individual or entity. The President shall periodically report a list of foreign individuals and entities that have knowingly engaged in, benefited from, or assisted in the significant theft of U.S. trade secrets that materially contributed to a significant threat to U.S. national security, foreign policy, or economic health. The report shall also list foreign individuals who are chief executive officers or board members of any foreign entity engaging in such theft. The President shall impose (1) property- and visa-blocking sanctions on individuals named in the report; and (2) property- or export-blocking sanctions, including denial of certain financial assistance, on entities named in the report.