In this paper, we examine the potential for a reconfigurable intelligent surface (RIS) to be powered by energy harvested from information signals. This feature might be key to reap the benefits of RIS technology's lower power consumption compared to active relays. We first identify the main RIS power-consuming components and then propose an energy harvesting and power consumption model. Furthermore, we formulate and solve the problem of the optimal RIS placement together with the amplitude and phase response adjustment of its elements in order to maximize the signal-to-noise ratio (SNR) while harvesting sufficient energy for its operation. Finally, numerical results validate the autonomous operation potential and reveal the range of power consumption values that enables it.