Unmanned aerial vehicles (UAVs) play an essential role in various applications, such as transportation and intelligent environmental sensing. However, due to camera motion and complex environments, it can be difficult to recognize the UAV from its surroundings thus, traditional methods often miss detection of UAVs and generate false alarms. To address these issues, we propose a novel method for detecting and tracking UAVs. First, a cross-scale feature aggregation CenterNet (CFACN) is constructed to recognize the UAVs. CFACN is a free anchor-based center point estimation method that can effectively decrease the false alarm rate, the misdetection of small targets, and computational complexity. Secondly, the region of interest-scale-crop-resize (RSCR) method is utilized to merge CFACN and region-of-interest (ROI) CFACN (ROI-CFACN) further, in order to improve the accuracy at a lower computational cost. Finally, the Kalman filter is adopted to track the UAV. The effectiveness of our method is validated using a collected UAV dataset. The experimental results demonstrate that our methods can achieve higher accuracy with lower computational cost, being superior to BiFPN, CenterNet, YoLo, and their variants on the same dataset.