The idea of using a Reconfigurable Intelligent Surface (RIS) consisting of a large array of passive scattering elements to assist wireless communication systems has recently attracted much attention from academia and industry. A central issue with RIS is how much power they can effectively convey to the target radio nodes. Regarding this question, several power level models exist in the literature but few have been validated through experiments. In this paper, we propose a radar cross section-based received power model for an RIS-aided wireless communication system that is rooted in the physical properties of RIS. Our proposed model follows the intuition that the received power is related to the distances from the transmitter/receiver to the RIS, the angles in the TX-RIS-RX triangle, the effective area of each element, and the reflection coefficient of each element. To the best of our knowledge, this paper is the first to model the angle-dependent phase shift of the reflection coefficient, which is typically ignored in existing literature. We further measure the received power with our experimental platform in different scenarios to validate our model. The measurement results show that our model is appropriate both in near field and far field and can characterize the impact of angles well.