Partner with Korea Act This bill creates an E-4 nonimmigrant visa category for up to 15,000 nationals of South Korea each fiscal year who are coming to the United States solely to perform specialty occupation services, subject to various requirements. The 15,000 limit shall only apply to principal recipients of such visas and not their accompanying spouses or children. (A specialty occupation is one that requires the theoretical and practical application of highly specialized knowledge and a bachelor's degree or higher.)