In a point cloud sequence, 3D object tracking aims to predict the location and orientation of an object in the current search point cloud given a template point cloud. Motivated by the success of transformers, we propose Point Tracking TRansformer (PTTR), which efficiently predicts high-quality 3D tracking results in a coarse-to-fine manner with the help of transformer operations. PTTR consists of three novel designs. 1) Instead of random sampling, we design Relation-Aware Sampling to preserve relevant points to given templates during subsampling. 2) Furthermore, we propose a Point Relation Transformer (PRT) consisting of a self-attention and a cross-attention module. The global self-attention operation captures long-range dependencies to enhance encoded point features for the search area and the template, respectively. Subsequently, we generate the coarse tracking results by matching the two sets of point features via cross-attention. 3) Based on the coarse tracking results, we employ a novel Prediction Refinement Module to obtain the final refined prediction. In addition, we create a large-scale point cloud single object tracking benchmark based on the Waymo Open Dataset. Extensive experiments show that PTTR achieves superior point cloud tracking in both accuracy and efficiency. Code will be made available at https://github.com/Jasonkks/PTTR.