Unmanned aerial vehicle (UAV) as an aerial base station is a promising technology to rapidly provide wireless connectivity to ground users. Given UAV's agility and mobility, a key question is how to adapt UAV deployment to best cater to the instantaneous wireless traffic in a territory. In this paper, we propose an adaptive deployment scheme for a UAV-aided communication network, where the UAV adapts its displacement direction and distance to serve randomly moving users' instantaneous traffic in the target cell. In our adaptive scheme, the UAV does not need to learn users' exact locations in real time, but chooses its displacement direction based on a simple majority rule by flying to the spatial sector with the greatest number of users in the cell. To balance the service qualities of the users in different sectors, we further optimize the UAV's displacement distance in the chosen sector to maximize the average throughput and the successful transmission probability, respectively. We prove that the optimal displacement distance for average throughput maximization decreases with the user density: the UAV moves to the center of the chosen sector when the user density is small and the UAV displacement becomes mild when the user density is large. In contrast, the optimal displacement distance for success probability maximization does not necessarily decrease with the user density and further depends on the target signal-to-noise ratio (SNR) threshold. Extensive simulations show that the proposed adaptive deployment scheme outperforms the traditional non-adaptive scheme, especially when the user density is not large.