Accountability for Persistent Intellectual Property Theft Act This bill directs the President to impose visa- and property-blocking sanctions on certain Chinese nationals and entities that knowingly engage in a pattern of significant theft of intellectual property belonging to a U.S. individual or entity. Specifically, these sanctions shall apply to (1) each Chinese national engaging in such theft who is not a U.S. national or permanent resident, (2) each entity engaging in such theft that is organized under Chinese law or owned by a Chinese national, and (3) each non-U.S. entity or individual engaging in such theft under the direction of a Chinese national or entity organized under Chinese law.