Tracking 3D objects is an important task in autonomous driving. Classical Kalman Filtering based methods are still the most popular solutions. However, these methods require handcrafted designs in motion modeling and can not benefit from the growing data amounts. In this paper, Box Only Transformer Tracker (BOTT) is proposed to learn to link 3D boxes of the same object from the different frames, by taking all the 3D boxes in a time window as input. Specifically, transformer self-attention is applied to exchange information between all the boxes to learn global-informative box embeddings. The similarity between these learned embeddings can be used to link the boxes of the same object. BOTT can be used for both online and offline tracking modes seamlessly. Its simplicity enables us to significantly reduce engineering efforts required by traditional Kalman Filtering based methods. Experiments show BOTT achieves competitive performance on two largest 3D MOT benchmarks: 69.9 and 66.7 AMOTA on nuScenes validation and test splits, respectively, 56.45 and 59.57 MOTA L2 on Waymo Open Dataset validation and test splits, respectively. This work suggests that tracking 3D objects by learning features directly from 3D boxes using transformers is a simple yet effective way.