Aircraft classification in synthetic aperture radar (SAR) images plays a considerable role in global region management and surveillance. Recently, deep learning has been applied to solve the classification problem and made significant progress. Due to the imaging variability at different angles and component scattering discreteness in SAR images, previous works have had difficulty in achieving desirable classification results. To address these issues, we study the positional and semantic relationship between the scattering points and propose an innovative scattering topology network (ST-Net) in this article. First, considering the diversity of imaging results caused by different target attitude angles, we extract and transform the scattering cluster centers to update the information of various categories. It can guide the model to strengthen the discriminative features and mitigate the impact of imaging variability on classification performance. Second, a novel scattering topology module (STM) is introduced to model the spatial relationships and semantic information interaction of discrete scattering points. In this process, the topology relations and scattering characteristics are enhanced for further accurate classification. Third, context attention excitation (CAE) is designed to capture significant global and semantic information, which is conducive to suppressing background interference and reducing category confusion. In conclusion, the ST-Net is presented with the SAR imaging mechanism and the topology geometric representation of aircraft. We construct the SAR aircraft category dataset (SAR-ACD) and conduct extensive experiments on it to show the effectiveness of ST-Net, which illustrates that our method achieves superior classification performance.