Reconfigurable Intelligent Surface (RIS) has grown rapidly due to its performance improvement for wireless networks, and the integration of unmanned aerial vehicle (UAV) and RIS has obtained widespread attention. In this paper, the downlink of non-orthogonal multiple access (NOMA) UAV networks equipped with RIS is considered. The objective is to optimize the UAV trajectory with RIS phase shift to maximize the system capacity under the UAV energy consumption constraint. By deep reinforcement learning, a capacity maximization scheme under energy consumption constraints based on double deep Q-Network (DDQN) is proposed. The joint optimization of UAV trajectory with RIS phase shift design is achieved by DDQN algorithm. From the numerical results, the proposed optimization scheme can increase the system capacity of the RIS-UAV-assisted NOMA networks.