Partner with Korea Act - Amends the Immigration and Nationality Act to create an E-4 treaty trader visa category for up to 15,000 nationals of the Republic of Korea (South Korea) each fiscal year who are coming to the United States solely to perform specialty occupation services and with respect to whom the Secretary of Labor has certified to the Secretary of Homeland Security (DHS) and the Secretary of State that the intending employer has filed an attestation concerning U.S. worker protections with the Secretary of Labor.