The pervasiveness of location-acquisition technologies enable location-based social networks (LBSN) to become increasingly popular in recent years. Users are able to check-in their current location and share information with other users through these networks. LBSN check-in data can be used for the benefit of users by providing personalized recommendations. There are several location recommendation algorithms that employ LBSN data in the literature. However, there are few number of proposed activity recommendation algorithms. In this paper, we propose a random walk based context-aware activity recommendation algorithm, namely RWCAR, for LBSNs. RWCAR considers the current context (i.e. social relations, personal preferences, and current location) of the user to provide recommendations. We propose a graph model for representing LBSN data that contains users, locations and activities. We build a graph according to the current context of the user depending on this LBSN model. A random walk approach is employed to predict the recommendation scores of the activities. A list of activities are recommended in decreasing order of calculated recommendation score. In experimental evaluation, we compare RWCAR with friend-based, expert-based and popularity-based activity recommendation algorithms. The proposed algorithm performs better in terms of activity recommendation accuracy in all of the experiments.