Recently, movable antenna (MA) array becomes a promising technology for improving the communication quality in wireless communication systems. In this letter, an unmanned aerial vehicle (UAV) enabled multi-user multi-input-single-output system enhanced by the MA array is investigated. To enhance the throughput capacity, we aim to maximize the achievable data rate by jointly optimizing the transmit beamforming, the UAV trajectory, and the positions of the MA array antennas. The formulated data rate maximization problem is a highly coupled non-convex problem, for which an alternating optimization based algorithm is proposed to get a sub-optimal solution. Numerical results have demonstrated the performance gain of the proposed method compared with conventional method with fixed-position antenna array.