Social recommendation has shown promising improvements over traditional systems since it leverages social correlation data as an additional input. Most existing work assumes that all data are available to the recommendation platform. However, in practice, user-item interaction data (e.g.,rating) and user-user social data are usually generated by different platforms, and both of which contain sensitive information. Therefore, "How to perform secure and efficient social recommendation across different platforms, where the data are highly-sparse in nature" remains an important challenge. In this work, we bring secure computation techniques into social recommendation, and propose S3Rec, a sparsity-aware secure cross-platform social recommendation framework. As a result, our model can not only improve the recommendation performance of the rating platform by incorporating the sparse social data on the social platform, but also protect data privacy of both platforms. Moreover, to further improve model training efficiency, we propose two secure sparse matrix multiplication protocols based on homomorphic encryption and private information retrieval. Our experiments on two benchmark datasets demonstrate the effectiveness of S3Rec.