The inherent unknown deformations of inverse synthetic aperture radar (ISAR) images, such as translation, scaling, and rotation, pose great challenges to space target classification. To achieve high-precision classification for ISAR images, a deformation-robust ISAR image classification network using contrastive learning (CL), i.e., CLISAR-Net, is proposed for deformation ISAR image classification. Unlike traditional supervised learning methods, CLISAR-Net develops a new unsupervised pretraining phase, which means that the method uses a two-phase training strategy to achieve classification. In the unsupervised pretraining phase, combined with data augmentation, positive and negative sample pairs are constructed using unlabeled ISAR images, and then the encoder is trained to learn discriminative deep representations of deformation ISAR images by means of CL. In the fine-tuning phase, based on the deep representations obtained from pretraining, a classifier is fine-tuned using a small number of labeled ISAR images, and finally, the deformation ISAR image classification is realized. In the experimental analysis, CLISAR-Net achieves higher classification accuracy than supervised learning methods for unknown scaled, rotated, and combined deformations. It implies that CLISAR-Net learned more robust deep features of deformation ISAR images through CL, which ensures the performance of the subsequent classification.