This letter studies a wireless system consisting of distributed ground terminals (GTs) communicating with an unmanned aerial vehicle (UAV) that serves as a mobile base station (BS). The UAV flies cyclically above the GTs at a fixed altitude, which results in a cyclical pattern of the strength of the UAV-GT channels. To exploit such periodic channel variations, we propose a new cyclical multiple access (CMA) scheme to schedule the communications between the UAV and GTs in a cyclical time-division manner based on the flying UAV's position. The time allocations to different GTs are optimized to maximize their minimum throughput. It is revealed that there is a fundamental tradeoff between throughput and access delay in the proposed CMA. Simulation results show significant throughput gains over the case of a static UAV BS in delay-tolerant applications.