A large body of work has been devoted to address corporate-scale privacy concerns related to social networks. The main focus was on how to share social networks owned by organizations without revealing the identities or sensitive relationships of the users involved. Not much attention has been given to the privacy risk of users posed by their information sharing activities. In this paper, we approach the privacy concerns arising in online social networks from the individual users' viewpoint: we propose a framework to compute a privacy score of a user, which indicates the potential privacy risk caused by his participation in the network. Our definition of privacy score satisfies the following intuitive properties: the more sensitive the information revealed by a user, the higher his privacy risk. Also, the more visible the disclosed information becomes in the network, the higher the privacy risk. We develop mathematical models to estimate both sensitivity and visibility of the information. We apply our methods to synthetic and real-world data and demonstrate their efficacy and practical utility.