Online platforms can be divided into information-oriented and social-oriented domains. The former refers to forums or E-commerce sites that emphasize user-item interactions, like Trip.com and Amazon; whereas the latter refers to social networking services (SNSs) that have rich user-user connections, such as Facebook and Twitter. Despite their heterogeneity, these two domains can be bridged by a few overlapping users, dubbed as bridge users. In this work, we address the problem of cross-domain social recommendation, i.e., recommending relevant items of information domains to potential users of social networks. To our knowledge, this is a new problem that has rarely been studied before. Existing cross-domain recommender systems are unsuitable for this task since they have either focused on homogeneous information domains or assumed that users are fully overlapped. Towards this end, we present a novel Neural Social Collaborative Ranking (NSCR) approach, which seamlessly sews up the user-item interactions in information domains and user-user connections in SNSs. In the information domain part, the attributes of users and items are leveraged to strengthen the embedding learning of users and items. In the SNS part, the embeddings of bridge users are propagated to learn the embeddings of other non-bridge users. Extensive experiments on two real-world datasets demonstrate the effectiveness and rationality of our NSCR method.