To tackle the inherent unknown deformation (e.g., translation, rotation and scaling) of the inverse synthetic aperture radar (ISAR) images, a deep polar transformer-circular convolutional neural network, i.e., PT-CCNN, is proposed to achieve deformation robust ISAR image automatic target recognition (ATR) in this paper. Inspired by human visual system and canonical coordinate of Lie-groups, we adopt a polar transformer module to transform the deformation ISAR images to the log-polar representations, before which a conventional convolutional neural network (CNN) is utilized to predict the origin of log-polar transformation. The above techniques make the proposed network invariant to translation, and equivariant to rotation and scaling. On this basis, for the log-polar representations with wrap-around structure, a circular convolutional neural network (CCNN) is further applied to extract more effective and highly discriminative features and improve recognition accuracy. The proposed network is end-to-end trainable with a classification loss, and could extract deformation-robust and essential features automatically. For multiple practical ISAR image datasets of six satellites, the performance testing and comparison experiments demonstrate that the techniques utilized in PT-CCNN are effective, and our proposed network achieve higher recognition accuracy than those previous common methods based on deep learning. For instance, our proposed PT-CCNN beats traditional CNN on rotation, scaling and practical deformation datasets by 24.5-49.3%, 9.0-40.8% and 22.3-26.7%. And it also outperforms the polar CNN without using the above techniques on rotation, scaling and practical deformation datasets by 9.2-53.7%, 5.2-54.6% and 9.0-49.9%. Additionally, the presented visualization results show the abilities and advantages of our method in terms of handling image deformation and extracting effective features.INDEX TERMS Automatic target recognition (ATR), inverse synthetic aperture radar (ISAR), deep convolutional neural network (DCNN), image deformation, log-polar transformation.