In this paper, optimal power control policies for an interference channel with two energy harvesting transmitters and two corresponding receivers are considered. Energy harvesting transmitters have strict power constraints due to the harvesting process as well as battery capacity constraints. The derived optimal power policies maximize the sum-throughput of a deadline constrained system under such energy and data arrival constraints by utilizing the limited available energy and managing the interference in the channel simultaneously. It is shown that an alternating maximization approach that individually optimizes the power policies for each transmitter in a cyclic manner converges to the optimal policy. The single-user subproblems with data constraints are solved using a generalized directional water-filling algorithm. A practical distributed algorithm requiring only local energy harvesting information is presented, and its near-optimal performance is demonstrated through simulations.