Differential privacy is effective in sharing information and preserving privacy with a strong guarantee. As social network analysis has been extensively adopted in many applications, it opens a new arena for the application of differential privacy. In this article, we provide a comprehensive survey connecting the basic principles of differential privacy and applications in social network analysis. We present a concise review of the foundations of differential privacy and the major variants and discuss how differential privacy is applied to social network analysis, including privacy attacks in social networks, types of differential privacy in social network analysis, and a series of popular tasks, such as degree distribution analysis, subgraph counting and edge weights. We also discuss a series of challenges for future studies.