Monitoring swimmer performance is crucial for improving training and enhancing athletic techniques. Traditional methods for tracking swimmers, such as above-water and underwater cameras, face limitations due to the need for multiple cameras and obstructions from water splashes. This paper presents a novel approach for tracking swimmers using a moving UAV. The proposed system employs a UAV equipped with a high-resolution camera to capture aerial footage of the swimmers. The footage is then processed using computer vision algorithms to extract the swimmers' positions and movements. This approach offers several advantages, including single camera use and comprehensive coverage. The system's accuracy is evaluated with both training and in competition videos. The results demonstrate the system's ability to accurately track swimmers' movements, limb angles, stroke duration and velocity with the maximum error of 0.3 seconds and 0.35~m/s for stroke duration and velocity, respectively.