While 6D object pose estimation has wide applications across computer vision and robotics, it remains far from being solved due to the lack of annotations. The problem becomes even more challenging when moving to category-level 6D pose, which requires generalization to unseen instances. Current approaches are restricted by leveraging annotations from simulation or collected from humans. In this paper, we overcome this barrier by introducing a self-supervised learning approach trained directly on large-scale real-world object videos for category-level 6D pose estimation in the wild. Our framework reconstructs the canonical 3D shape of an object category and learns dense correspondences between input images and the canonical shape via surface embedding. For training, we propose novel geometrical cycle-consistency losses which construct cycles across 2D-3D spaces, across different instances and different time steps. The learned correspondence can be applied for 6D pose estimation and other downstream tasks such as keypoint transfer. Surprisingly, our method, without any human annotations or simulators, can achieve on-par or even better performance than previous supervised or semi-supervised methods on in-the-wild images. Code and videos are available at https://kywind.github.io/self-pose.