No Social Media Accounts for Terrorists or State Sponsors of Terrorism Act of 2021 This bill bars access to certain social media platforms by individuals designated as terrorists or senior officials of a government that is a state sponsor of terrorism. Specifically, the bill requires the President to prohibit providers of social media platforms (i.e., platforms that allow users to generate and share content and that have over 100,000 active users) from making such platforms available to barred individuals or officials. The bill does, however, allow officials to use these platforms solely for legitimate emergency alert purposes. Violations of this prohibition are subject to civil and criminal penalties. In addition, the President may waive the prohibition in the interests of U.S. national security. The Department of the Treasury must report to Congress on (1) the status and impact of the prohibitions of this bill, and (2) efforts to facilitate the free flow of information and access to communications technologies by civil society and democratic activists in Iran, Syria, North Korea, Cuba, and other countries controlled by authoritarian regimes.