Despite the availability of multiple safe vaccines, vaccine hesitancy may present a challenge to successful control of the COVID-19 pandemic. As with many human behaviors, people’s vaccine acceptance may be affected by their beliefs about whether others will accept a vaccine (i.e., descriptive norms). However, information about these descriptive norms may have different effects depending on people’s baseline beliefs and the relative importance of conformity, social learning, and free-riding. Here, using a large, pre-registered, randomized experiment (N=437,236) embedded in an international survey, we show that accurate information about descriptive norms can substantially increase intentions to accept a vaccine for COVID-19. These positive effects (e.g., reducing by 5.3% the fraction of people who are “unsure” or more negative about accepting a vaccine) are largely consistent across the 23 included countries, but are concentrated among people who were otherwise uncertain about accepting a vaccine. Providing this normative information in vaccine communications partially corrects individuals’ apparent underestimation of how many other people will accept a vaccine. These results suggest that public health communications should present information about the widespread and growing intentions to accept COVID-19 vaccines.