As unmanned aerial vehicles (UAVs) become more accessible with a growing range of applications, the potential risk of UAV disruption increases. Recent development in deep learning allows vision-based counter-UAV systems to detect and track UAVs with a single camera. However, the coverage of a single camera is limited, necessitating the need for multi-camera configurations to match UAVs across cameras — a problem known as re-identification (reID). While there has been extensive research on person and vehicle reID to match objects across time and viewpoints, to the best of our knowledge, there has been no research in UAV reID. UAVs are challenging to re-identify: they are much smaller than pedestrians and vehicles and they are often detected in the air so appear at a greater range of angles. Because no UAV data sets currently use multiple cameras, we propose the first new UAV re-identification data set, UAV-reID, that facilitates the development of machine learning solutions in this emerging area. UAV-reID has two settings: Temporally-Near to evaluate performance across views to assist tracking frameworks, and Big-to-Small to evaluate reID performance across scale and to allow early reID when UAVs are detected from a long distance. We conduct a benchmark study by extensively evaluating different reID backbones and loss functions. We demonstrate that with the right setup, deep networks are powerful enough to learn good representations for UAVs, achieving 81.9% mAP on the Temporally-Near setting and 46.5% on the challenging Big-to-Small setting. Furthermore, we find that vision transformers are the most robust to extreme variance of scale.