The fast advancement of unmanned aerial vehicle (UAV) technology has facilitated its use across a wide range of scenarios. Due to the high mobility and flexibility of drones, the images they capture often exhibit significant scale variations and severe object occlusions, leading to a high density of small objects. However, the existing object detection algorithms struggle with detecting small objects effectively in cross-scale detection scenarios. To overcome these difficulties, we introduce a new object detection model, RPS-YOLO, based on the YOLOv8 architecture. Unlike the existing methods that rely on traditional feature pyramids, our approach introduces a recursive feature pyramid (RFP) structure. This structure performs two rounds of feature extraction, and we reduce one downsampling step in the first round to enhance attention to small objects during cross-scale detection. Additionally, we design a novel attention mechanism that improves feature representation and mitigates feature degradation during convolution by capturing spatial- and channel-specific details. Another key innovation is the proposed Localization IOU (LIOU) loss function for bounding box regression, which accelerates the regression process by incorporating angular constraints. Experiments conducted on the VisDrone-DET2021 and UAVDT datasets show that RPS-YOLO surpasses YOLOv8s, with an mAP50 improvement of 8.2% and 3.4%, respectively. Our approach demonstrates that incorporating recursive feature extraction and exploiting detailed information for multi-scale detection significantly improves detection performance, particularly for small objects in UAV images.