In recent years, unmanned aerial vehicles (UAVs) have become a valuable platform for many applications, including communication networks. UAV-enabled wireless communication faces challenges in complex urban and dynamic environments. UAVs can suffer from power limitations and path losses caused by non-line-of-sight connections, which may hamper communication performance. To address these issues, reconfigurable intelligent surfaces (RIS) have been proposed as helpful technologies to enhance UAV communication networks. However, due to the high mobility of UAVs, complex channel environments, and dynamic RIS configurations, it is challenging to estimate the link quality of ground users. In this paper, we propose a link quality estimation model using a gated recurrent unit (GRU) to assess the link quality of ground users for a multi-user RIS-assisted UAV-enabled wireless communication system. Our proposed framework uses a time series of user channel data and RIS phase shift information to estimate the quality of the link for each ground user. The simulation results showed that the proposed GRU model can effectively and accurately estimate the link quality of ground users in the RIS-assisted UAV-enabled wireless communication network.