Inspired by the recent PointHop classification method, an unsupervised 3D point cloud registration method, called R-PointHop, is proposed in this work. R-PointHop first determines a local reference frame (LRF) for every point using its nearest neighbors and finds its local attributes. Next, R-PointHop obtains local-to-global hierarchical features by point downsampling, neighborhood expansion, attribute construction and dimensionality reduction steps. Thus, we can build the correspondence of points in the hierarchical feature space using the nearest neighbor rule. Afterwards, a subset of salient points of good correspondence is selected to estimate the 3D transformation. The use of LRF allows for hierarchical features of points to be invariant with respect to rotation and translation, thus making R-PointHop more robust in building point correspondence even when rotation angles are large. Experiments are conducted on the ModelNet40 and the Stanford Bunny dataset, which demonstrate the effectiveness of R-PointHop on the 3D point cloud registration task. R-PointHop is a green and accurate solution since its model size and training time are smaller than those of deep learning methods by an order of magnitude while its registration errors are smaller. Our codes are available on GitHub.