This paper presents an event-triggered controller that solves the problem of trajectory tracking for an aerial vehicle with thrust actuation in a single body-fixed direction and full angular velocity actuation. Firstly, we design a globally stabilizing hybrid controller and then, using the framework of hybrid dynamical systems, we derive an appropriate event-triggering mechanism for sampling actuation signals. We prove the global asymptotic stability of a zero tracking error set for the closed-loop system. For practical implementation of the proposed event-triggered controller on digital platforms, we restrict the event-triggering condition and inflate the zero tracking error set to avoid Zeno solutions while achieving global asymptotic stability of the inflated set for the closed-loop system. The results are illustrated by numerical simulations and further verified by experiments.