Deploying energy harvesting nodes can significantly extend the lifetime of a battery powered wireless network. The nature of these systems calls for specific design principles to efficiently utilize the dynamic energy resources. In contrast to the conventional wireless networks, transmission policies for these systems should take into account the recharge process of the node as well as its battery capacity. In this work, we focus on the problem of finding the optimal transmission policy to maximize the short-term throughput of an energy harvesting transmitter node with power control and a limited energy storage capacity. The transmission policy in this problem is strictly constrained with both the energy arrival process and the energy storage capacity of the node. The analysis of the problem is founded on the increasing concave nature of the power-rate relationship information theoretic findings suggest. A discrete model with packets of energy arrivals is considered for energy replenishment, and an algorithm to yield the short-term throughout maximizing policy is sought. The necessary conditions such a policy should satisfy are identified and an algorithm to yield the unique policy that satisfies these conditions is presented. The performance of this algorithm is then observed through numerical results.