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Point cloud classifiers with rotation robustness have been widely discussed in the 3D deep learning community. Most proposed methods either use rotation invariant descriptors as inputs or try to design rotation equivariant networks. However, robust models generated by these methods have limited performance under clean aligned datasets due to modifications on the original classifiers or input space. In this study, for the first time, we show that the rotation robustness of point cloud classifiers can also be acquired via adversarial training with better performance on both rotated and clean datasets. Specifically, our proposed framework named ART-Point regards the rotation of the point cloud as an attack and improves rotation robustness by training the classifier on inputs with Adversarial RoTations. We contribute an axis-wise rotation attack that uses back-propagated gradients of the pre-trained model to effectively find the adversarial rotations. To avoid model over-fitting on adversarial inputs, we construct rotation pools that leverage the transferability of adversarial rotations among samples to increase the diversity of training data. Moreover, we propose a fast one-step optimization to efficiently reach the final robust model. Experiments show that our proposed rotation attack achieves a high success rate and ART-Point can be used on most existing classifiers to improve the rotation robustness while showing better performance on clean datasets than state-of-the-art methods.