The exploitation of unmanned aerial vehicles (UAVs) as mobile relays to establish line-of-sight (LoS) links for free space optical (FSO) communications has shown significant potential. However, adverse weather conditions and pointing errors substantially affect the communication quality of FSO. Therefore, in this paper, an optical reconfigurable intelligent surface (ORIS)-assisted UAV relay FSO communications network is conceived, which is capable of adaptively offering high-quality communication services for mobile targets. To maximize the system’s ergodic capacity, a simulated annealing assisted double deep Q-network (SA-DDQN) method is proposed, which enhances system effectiveness by jointly optimizing the ORIS phase shift and UAV trajectory. Simulation results show that the proposed method is capable of adaptively formulating the trajectory of UAV in light of the user’s location and leads to an enhancement in ergodic capacity compared to the traditional UAV relay scheme under the same conditions.