Siamese trackers recently have achieved remarkable advancements in accuracy, yet the further improvement is subject to semantic interferences. An potential reason may be the lack of prior information in visual tracking. The final response map used for target location in a Siamese tracker represents the similarity associations between the target and dense image patches in search branch, which happens to be a kind of natural prior information. In this paper, we propose a self-aware circular response-guided attention for Siamese tracking from the angle how to use the implicit information in response maps. Firstly, a multi-level self-aware circular framework embedded in Siamese network is designed to fuse multi-level network features and prior information for more effective information integration. Specifically, these prior information, i.e., multi-level spatial and channel attentions, are exploited from multi-level response maps respectively via densely structured spatial attention module (DSSA) and bottom-up channel attention module (BUCA). Besides, DSSA absorbs a consistent sparse constraint term to strengthen the association of multi-level response maps. The experiments show that our SC-Siam and SC-Siam-ResNet trackers (with SiamDWFC and Siam-ResNet as baselines) achieve state-of-the-art performance on seven benchmarks, including OTB2013, OTB2015, VOT2016, VOT2018, VOT2020, GOT10K, and LASOT.