The rigid registration of aortic Digital Subtraction Angiography (DSA) and Computed Tomography Angiography (CTA) can provide 3D anatomical details of the vasculature for the interventional surgical treatment of conditions such as aortic dissection and aortic aneurysms, holding significant value for clinical research. However, the current methods for 2D/3D image registration are dependent on manual annotations or synthetic data, as well as the extraction of landmarks, which is not suitable for cross-modal registration of aortic DSA/CTA. In this paper, we propose an unsupervised method, UDCR, for aortic DSA/CTA rigid registration based on deep reinforcement learning. Leveraging the imaging principles and characteristics of DSA and CTA, we have constructed a cross-dimensional registration environment based on spatial transformations. Specifically, we propose an overlap degree calculation reward function that measures the intensity difference between the foreground and background, aimed at assessing the accuracy of registration between segmentation maps and DSA images. This method is highly flexible, allowing for the loading of pre-trained models to perform registration directly or to seek the optimal spatial transformation parameters through online learning. We manually annotated 61 pairs of aortic DSA/CTA for algorithm evaluation. The results indicate that the proposed UDCR achieved a Mean Absolute Error (MAE) of 2.85 mm in translation and 4.35{\deg} in rotation, showing significant potential for clinical applications.