In this paper, we investigate a reconfigurable intelligent surface (RIS)-assisted wireless communication system with energy harvesting. In the single information user (IU) scenario, we consider the power control of base station (BS) and the random deployment of energy users (EUs). To this end, we first characterize the statistical features of the channel gains over BS-RIS-IU and BS-RIS-EU cascaded links. Then, we derive a closed-form expression of the information outage probability (IOP) of the IU and show an upper bound of the energy outage probability (EOP) of EUs by invoking the Jensen's inequality. Furthermore, we consider two more general extensions, namely, the existence of imperfect phase alignment and multiple IUs. Finally, the correctness of the analysis results is verified by Monte-Carlo simulation.