Consider a multiple input-multiple output (MIMO) interference channel with partial channel state information (CSI) whereby the CSI is known only for some (or none) of the links, while the statistical knowledge is known for the remaining links. In this work, we consider the linear transceiver design problem for such an interference channel with partial CSI by maximizing the average long term sum-rate of the system. We propose an efficient stochastic sum-rate maximization algorithm based on the iterative optimization of the ensemble average of the sum rate utility function. The proposed algorithm can use the statistical knowledge of the links whenever the actual CSI is not available and is guaranteed to converge to the set of stationary points of the stochastic sum-rate maximization problem almost surely. The effectiveness and the efficiency of the proposed algorithm are validated via numerical experiments.