Unlike in natural images, in endoscopy there is no clear notion of an up-right camera orientation. Endoscopic videos therefore often contain large rotational motions, which require keypoint detection and description algorithms to be robust to these conditions. While most classical methods achieve rotation-equivariant detection and invariant description by design, many learning-based approaches learn to be robust only up to a certain degree. At the same time learning-based methods under moderate rotations often outperform classical approaches. In order to address this shortcoming, in this paper we propose RIDE, a learning-based method for rotation-equivariant detection and invariant description. Following recent advancements in group-equivariant learning, RIDE models rotation-equivariance implicitly within its architecture. Trained in a self-supervised manner on a large curation of endoscopic images, RIDE requires no manual labeling of training data. We test RIDE in the context of surgical tissue tracking on the SuPeR dataset as well as in the context of relative pose estimation on a repurposed version of the SCARED dataset. In addition we perform explicit studies showing its robustness to large rotations. Our comparison against recent learning-based and classical approaches shows that RIDE sets a new state-ofthe-art performance on matching and relative pose estimation tasks and scores competitively on surgical tissue tracking.