In this paper, we consider the performance of a mixed free-space optical and radio frequency (FSO-RF) relaying system with energy harvesting in the existence of both atmospheric turbulence and pointing errors. More specially, we assume that the direct current (DC) component of the FSO signal, which is generally filtered out, can be used for energy harvesting at the relay. We derive the exact closed-form expression for the outage probability of this setup in terms of the bivariate Fox-H function. We also provide the asymptotic analysis to obtain the diversity order. Finally, Monte-Carlo simulations are carried out to verify the correctness of our analytical results.