In this paper, a novel approach that uses an unmanned aerial vehicle (UAV)-carried intelligent reflector (IR) is proposed to enhance the performance of millimeter wave (mmW) networks. In particular, the UAV-IR is used to intelligently reflect mmW beamforming signals from a base station towards a mobile outdoor user, while harvesting energy from mmW signals to power the IR. To maintain a line-of-sight (LOS) channel, a reinforcement learning (RL) approach, based on Q-learning and neural networks, is proposed to model the propagation environment, such that the location and reflection coefficient of the UAV-IR can be optimized to maximize the downlink transmission capacity. Simulation results show a significant advantage for using a UAV-IR over a static IR, in terms of the average data rate and the achievable downlink LOS probability. The results also show that the RL-based deployment of the UAV-IR further improves the network performance, relative to a scheme without learning.