Synthetic aperture radar (SAR) has emerged as a critical technology for detecting and classifying objects such as ships in challenging environments. However, few-shot learning remains challenging due to the limited availability of labeled SAR data, complex radar backscatter, and variations in imaging parameters. In this paper, we propose a novel network, scattering point topology for few-shot ship classification (SPT-FSC), which addresses these challenges by incorporating scattering characteristics into the network learning process through a scattering point topology (SPT) based on scattering key points. We design a topology encoding branch (TEB) through a series of operations to encode the topological information of scattering points, resulting in a SPT embedding that improves the network's adaptability to the imaging mechanism and reduces imaging variability in SAR images. To effectively fuse the SPT embedding and image features extracted from a convolutional neural network (CNN), we introduce a novel mechanism named reciprocal feature fusion attention (RFFA). Additionally, to address the limited diversity in the training data, we apply fine-tuning based methodologies and construct a fine-grained ship classification dataset by combining the OpenSARShip and FUSAR-Ship datasets. Our comprehensive experiments on these datasets demonstrate the effectiveness of our proposed SPT-FSC method, achieving high accuracy and robustness in few-shot ship classification tasks for SAR images, outperforming existing methods in this domain.