In this paper, we propose an efficient solution for the privacy-preserving of a bipartite ranking algorithm. The bipartite ranking problem can be considered as finding a function that ranks positive instances (in a dataset) higher than the negative ones. However, one common concern for all the existing schemes is the privacy of individuals in the dataset. That is, one (e.g., a researcher) needs to access the records of all individuals in the dataset in order to run the algorithm. This privacy concern puts limitations on the use of sensitive personal data for such analysis. The RIMARC (Ranking Instances by Maximizing Area under the ROC Curve) algorithm solves the bipartite ranking problem by learning a model to rank instances. As part of the model, it learns weights for each feature by analyzing the area under receiver operating characteristic (ROC) curve. RIMARC algorithm is shown to be more accurate and efficient than its counterparts. Thus, we use this algorithm as a building-block and provide a privacy-preserving version of the RIMARC algorithm using homomorphic encryption and secure multi-party computation. Our proposed algorithm lets a data owner outsource the storage and processing of its encrypted dataset to a semi-trusted cloud. Then, a researcher can get the results of his/her queries (to learn the ranking function) on the dataset by interacting with the cloud. During this process, neither the researcher nor the cloud learns any information about the raw dataset. We prove the security of the proposed algorithm and show its efficiency via experiments on real data.