We investigate the uplink channel selection problem of unmanned aerial vehicle (UAV)-aided data collection system in delay-sensitive sensor networks. In the studied model, the fixed-wing UAV is dispatched to gather sensing information from terrestrial sensor nodes (SNs) and they contend for uplink channels for transmission. With the goal of minimizing the system-wide delay, we formulate a resource allocation problem. Encountered with the challenge that the flight trajectory of UAV is unknown to SNs and the wireless channel is time-varying, we solve the problem by stochastic game approach and further propose a fully distributed channel selection algorithm which is proved to converge to a pure strategy Nash Equilibrium (NE). Simulation results are presented to show that our proposed algorithm has good performance.