In this paper, we investigate the capacity of a point-to-point, full-duplex (FD), wirelessly powered communication system impaired by self-interference. This system is comprised of an energy transmitter (ET) and an energy harvesting user (EHU), both operating in a FD mode. The ET transmits energy towards the EHU. The EHU harvests this energy and uses it to transmit information back to the ET. As a result of the FD mode, both nodes are affected by self-interference. The self-interference has a different effect at the two nodes: it impairs the decoding of the received signal at the ET, however, it provides an additional source of energy for the EHU. This paper derives the capacity of this communication system assuming a processing cost at the EHU and additive white Gaussian noise channel with block fading. Thereby, we show that the capacity achieving scheme is relatively simple and therefore applicable to devices with limited resources. Moreover, our numerical results show significant improvements in terms of data rate when the capacity achieving strategy is employed compared to half-duplex transmission. Moreover, we show the positive and negative effects of the self-interference at the EHU and the ET, respectively. Furthermore, we show the crippling effect of the processing cost and demonstrate that failing to take it into consideration gives a false impression in terms of achievable rate.