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This paper proposes a self-supervised learning method for the person re-identification (re-ID) problem, where existing unsupervised methods usually rely on pseudo labels, such as those from video tracklets or clustering. A potential drawback of using pseudo labels is that errors may accumulate and it is challenging to estimate the number of pseudo IDs. We introduce a different unsupervised method that allows us to learn pedestrian embeddings from raw videos, without resorting to pseudo labels. The goal is to construct a self-supervised pretext task that matches the person re-ID objective. Inspired by the \emph{data association} concept in multi-object tracking, we propose the \textbf{Cyc}le \textbf{As}sociation (\textbf{CycAs}) task: after performing data association between a pair of video frames forward and then backward, a pedestrian instance is supposed to be associated to itself. To fulfill this goal, the model must learn a meaningful representation that can well describe correspondences between instances in frame pairs. We adapt the discrete association process to a differentiable form, such that end-to-end training becomes feasible. Experiments are conducted in two aspects: We first compare our method with existing unsupervised re-ID methods on seven benchmarks and demonstrate CycAs' superiority. Then, to further validate the practical value of CycAs in real-world applications, we perform training on self-collected videos and report promising performance on standard test sets.