Accurate 2D/3D integration of Digital Subtraction Angiography (DSA) and Computed Tomography Angiography (CTA) images holds significant potential for reducing risk for navigation in percutaneous coronary intervention (PCI). Rigid registration is a crucial step in achieving this integration. However, existing rigid registration methods based on manually designed features and subsequent rule-based graph matching exhibit limited generalization and often fail in complex surgical scenarios, such as vessel overlapping from 3D-to-2D projection and branch missing due to Chronic Total Occlusion (CTO). To address these challenges, we propose a vascular-topology-aware deep structure matching framework for 3D CTA and 2D DSA rigid registration. Our framework includes key-point extraction, where 2D/3D topological priors are used to extract key points and their descriptors, and a matching stage that employs a 3D spatial-aware hybrid attention mechanism to capture vessel structures while mitigating the impact of vessel overlap and branch missing on feature-based matching. We also designed a data simulation strategy to generate a large set of paired data for network training, using various rigid transformations and random branch trimming to simulate complex and variable real-world scenarios, especially the vessel overlap and branch missing. Extensive evaluations conducted on the simulated dataset and 1,016 pairs of real CTA and DSA samples demonstrate the effectiveness and robustness of our method, highlighting its strong performance and potential for real-world surgical applications. The code is available at https://github.com/sxxs666/2D-3DCoronary .