H-2B Returning Worker Exception Act of 2021 This bill modifies the H-2B (temporary nonagricultural workers) nonimmigrant visa program, including by exempting certain workers from an annual numerical limit on such visas and requiring civil penalties for program violations. Under this bill, if a worker seeking a H-2B visa has been counted toward the 66,000 annual cap on such visas in one of the three preceding fiscal years, that worker shall not be counted against the cap again. Furthermore, the Department of Homeland Security (DHS) must impose a civil monetary penalty on an employer for (1) failing to meet requirements related to an H-2B visa petition, or (2) making a willful misrepresentation of material fact in such a petition. DHS must also ensure the establishment of an electronic platform (1) for employers to submit and request approval of an H-2B petition, and (2) to act as a single point of access for applicants and the relevant government agencies. The Department of Labor must maintain a publicly available online database of all job orders by H-2B employers. Furthermore, Labor may take certain actions to enforce program requirements, such as imposing penalties and seeking injunctions. The bill provides statutory authority for the current practice of limiting the program to workers who are nationals of countries approved by DHS. DHS may make exceptions to this limitation in individual cases if it is in the U.S. interest to do so. DHS shall select approved countries based on various factors, such as the rate of overstay by H-2B visa holders from each country.