Feature invariance under different data transformations, i.e., transformation invariance, can be regarded as a type of self-supervision for representation learning. In this paper, we present PointClustering, a new unsupervised representation learning scheme that leverages transformation invariance for point cloud pre-training. PointClustering formulates the pretext task as deep clustering and employs transformation invariance as an inductive bias, following the philosophy that common point cloud transformation will not change the geometric properties and semantics. Technically, PointClustering iteratively optimizes the feature clusters and backbone, and delves into the transformation invariance as learning regularization from two perspectives: point level and instance level. Point-level invariance learning maintains local geometric properties through gathering point features of one instance across transformations, while instance-level invariance learning further measures clusters over the entire dataset to explore semantics of instances. Our PointClustering is architecture-agnostic and readily applicable to MLP-based, CNN-based and Transformer-based backbones. We empirically demonstrate that the models pre-learnt on the ScanNet dataset by PointClustering provide superior performances on six benchmarks, across downstream tasks of classification and segmentation. More remarkably, PointClustering achieves an accuracy of 94.5% on ModelNet40 with Transformer backbone. Source code is available at https://github.com/FuchenUSTC/PointClustering.