Safeguarding Educational Institutions, Colleges, Universities, and Research Entities from China's Attempts to Misappropriate Property of the United States Act of 2021 or the SECURE CAMPUS Act of 2021 This bill prohibits certain Chinese citizens from receiving visas to participate in graduate or post-graduate studies in science, technology, engineering, or math (STEM) and contains other related provisions. This prohibition applies to F (academic student) and J (exchange visitor) visas and does not apply to citizens or permanent residents of Taiwan or Hong Kong. (China considers Taiwan a Chinese province. Hong Kong is a special administrative region within China, and most of its permanent inhabitants are Chinese citizens.) The Department of State may waive this prohibition on a case-by-case basis for national security purposes or if the applicant is a member of a religious or ethnic group that is systematically oppressed by the Chinese Communist Party. Institutions of higher education in the federal Student and Exchange Visitor Program must annually certify that no prohibited Chinese citizens are permitted to participate in the institution's graduate or post-graduate STEM programs. A recipient of a federal STEM research grant must certify that the recipient (1) is not a Chinese citizen or a participant in a Chinese government foreign researcher recruitment program (a program that compensates individuals to conduct STEM-related research and development), and (2) will not knowingly use grant funds to employ such an individual. Entities that receive certain federal research or education assistance shall not knowingly employ any individual participating in a Chinese government foreign researcher recruitment program. An individual who recruits or performs research for such a program must register as an agent of a foreign principal.