The limitations of existing Synthetic Aperture Radar (SAR) Automatic Target Recognition (ATR) methods lie in their confinement by the closed-environment assumption, hindering their effective and robust handling of unknown target categories in open environments. Open Set Recognition (OSR), a pivotal facet for algorithmic practicality, intends to categorize known classes while denoting unknown ones as "unknown." The chief challenge in OSR involves concurrently mitigating risks associated with generalizing features from a restricted set of known classes to numerous unknown samples and the open space exposure to potential unknown data. To enhance open-set SAR classification, a method called scattering kernel with reciprocal learning network is proposed. Initially, a feature learning framework is constructed based on reciprocal point learning (RPL), establishing a bounded space for potential unknown classes. This approach indirectly introduces unknown information into a learner confined to known classes, thereby acquiring more concise and discriminative representations. Subsequently, considering the variability in the imaging of targets at different angles and the discreteness of components in SAR images, a proposal is made to design convolutional kernels based on large-sized attribute scattering center models. This enhances the ability to extract intrinsic non-linear features and specific scattering characteristics in SAR images, thereby improving the discriminative features of the model and mitigating the impact of imaging variations on classification performance. Experiments on the MSTAR datasets substantiate the superior performance of the proposed approach called ASC-RPL over mainstream methods.