This paper considers a single-hop wireless sensor network where a fusion center (FC) collects data from M energy harvesting (EH) wireless sensor nodes. The harvested energy is stored losslessly in an infinite-capacity battery at each node. In each time slot, K nodes can be scheduled by the FC to send data over K orthogonal channels. The FC has no direct knowledge on the battery states of nodes, or the statistics of EH processes; it only has information of the outcomes of previous transmission attempts. The objective is to find a simple policy whereby maximum total throughput is achieved in this data back-logged system. A node can transmit data whenever being scheduled, provided it has sufficient energy for transmission. A simple policy, Uniforming Random Ordered Policy (UROP), is proposed for the problem. UROP is proved to be asymptotically optimal over infinite time horizon for general EH processes. Numerical results indicate that even with finite-capacity batteries, UROP achieves near-optimal throughput. We believe that UROP is applicable to a wider area than EH wireless sensor networks.