Cultural heritage tourism, as a typical integration of culture and tourism, has attracted extensive attention in recent years. Although some scholars have already explored the influencing mechanism of tourists’ behavioral intention in cultural heritage destinations, there remains a lack of research on how the social responsibility of cultural heritage tourism destinations affects tourist citizenship behavior. Exploring the formation mechanism of tourist citizenship behavior at cultural heritage sites from the perspective of destination social responsibility, this study intends to provide a theoretical reference for realizing the high-quality development of cultural heritage tourism. In this study, a chain mediation model based on destination reputation and destination identification is constructed to clarify the influencing mechanism of destination social responsibility on tourist citizenship behavior. The structural equation model and bootstrapping methods are applied to conduct empirical tests on 573 valid samples who have experienced cultural heritage tourism. The results show that: (a) the social responsibility of cultural heritage destinations positively affects the tourist citizenship behavior; (b) the destination reputation plays a mediating role between destination social responsibility and tourist advocacy behavior; (c) the destination identification plays a mediating role between destination social responsibility and tourist feedback behavior and tourist advocacy behavior; (d) the destination reputation and destination identification jointly play a chain mediation role between destination social responsibility and tourist citizenship behavior. These research results not only clarify the internal mechanism between the social responsibility of cultural heritage sites and tourist citizenship behavior, but also presented certain significance for practically guiding the destination managers to promote the sustainable development of cultural heritage tourism.