With the explosive increase in demand for wireless communication, the issue of wireless communication security has also become a growing concern. In this paper, we investigate a novel covert communication for unmanned aerial vehicle (UAV)-assisted uplink rate-splitting multiple access (RSMA) systems, where a UAV adopts the rate-splitting (RS) strategy to increase the total transmission rate while avoiding deteriorating the covert transmission of a ground user. In the proposed system, a ground user and a UAV adopt the RSMA scheme to simultaneously communicate with a base station surveilled by an evil monitor. The UAV acts as both the transmitter and the friendly jammer to cover the ground user’s transmission with random power. To maximize the expected sum rate (ESR), we first study the RS strategy and obtain the optimal power allocation factor. Then, the closed-form of minimum detection error probability (DEP), ESR, and optimal target rate of the UAV are derived. Constrained by the minimum DEP and expected covert rate (ECR), we maximize the ESR by optimizing the position and target rate of the UAV. Numerical results show that the proposed scheme outperforms the traditional NOMA systems in terms of ESR with the same DEP and ECR.