Morphological segmentation of the aorta is significant for aortic diagnosis, intervention, and prognosis. However, it is difficult for existing methods to achieve the continuity of spatial information and the integrity of morphological extraction, due to the gradually variable and irregular geometry of the aorta in the long-sequence computed tomography (CT). In this paper, we propose a geometry-constrained deformable attention network (GDAN) to learn the aortic common features through interaction with context information of the anatomical space. The deformable attention extractor in our model can adaptively adjust the position and the size of patches to match different shapes of the aorta. The self-attention mechanism is also helpful to explore the long-range dependency in CT sequences and capture more semantic features. The geometry-constrained guider simplifies the morphological representation with a high spatial similarity. The guider imposes strong constraints on geometric boundaries, which changes the sensitivity of gradually variable aortic morphology in the network. Guider can assist the correct extraction of semantic features combining deformable attention extractor. In 204 cases of aortic CT dataset, including 42 normal aorta, 45 coarctation of the aorta, and 107 aortic dissection, our method obtained a mean dice similarity coefficient of 0.943 on the test set (20%), outperforming 6 state-of-the-art methods about aortic segmentation.