Object tracking approaches based on the Siamese network have demonstrated their huge potential in the remote sensing field recently. Nevertheless, due to the limited computing resource of aerial platforms and special challenges in aerial tracking, most existing Siamese-based methods can hardly meet the real-time and state-of-the-art performance simultaneously. Consequently, a novel Siamese-based method is proposed in this work for onboard real-time aerial tracking, i.e., SiamAPN. The proposed method is a no-prior two-stage method, i.e., Stage-1 for proposing adaptive anchors to enhance the ability of object perception and Stage-2 for fine-tuning the proposed anchors to obtain accurate results. Distinct from the traditional predefined anchors, the proposed anchors can adapt automatically to the tracking object. Besides, the internal information of adaptive anchors is utilized to feedback SiamAPN for enhancing the object perception. Attributing to the feature fusion network, different semantic information is integrated, enriching the information flow that is significant for robust aerial tracking. In the end, the regression and multiclassification operation refine the proposed anchors meticulously. Comprehensive evaluations on three well-known aerial tracking benchmarks have proven the superior performance of the presented approach. Moreover, to verify the practicability of the proposed method, SiamAPN is implemented onboard a typical embedded aerial tracking platform to conduct the real-world evaluations on specific aerial tracking scenarios, e.g., fast motion, long-term tracking, and low resolution. The results have demonstrated the efficiency and accuracy of the proposed approach, with a processing speed of over 30 frames/s. In addition, the image sequences in the real-world evaluations are collected and annotated as a new aerial tracking benchmark, i.e., UAVTrack112.