3D object trackers usually require training on large amounts of annotated data that is expensive and time-consuming to collect. Instead, we propose leveraging vast unlabeled datasets by self-supervised metric learning of 3D object trackers, with a focus on data association. Large scale annotations for unlabeled data are cheaply obtained by automatic object detection and association across frames. We show how these self-supervised annotations can be used in a principled manner to learn point-cloud embeddings that are effective for 3D tracking. We estimate and incorporate uncertainty in self-supervised tracking to learn more robust embeddings, without needing any labeled data. We design embeddings to differentiate objects across frames, and learn them using uncertainty-aware self-supervised training. Finally, we demonstrate their ability to perform accurate data association across frames, towards effective and accurate 3D tracking. Project videos and code are at https://jianrenw.github.io/Self-Supervised-3D-Data-Association/.