Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. Recent works achieve good performance relying on a large amount of expensive-to-obtain labeled data. To reduce the amount of supervision, we for the first time propose a general framework, FisherMatch, for semi-supervised rotation regression, without assuming any domain-specific knowledge or paired data. Inspired by the popular semi-supervised approach, FixMatch, we propose to leverage pseudo label filtering to facilitate the information flow from labeled data to unlabeled data in a teacher-student mutual learning framework. However, incorporating the pseudo label filtering mechanism into semi-supervised rotation regression is highly non-trivial, mainly due to the lack of a reliable confidence measure for rotation prediction. In this work, we propose to leverage matrix Fisher distribution to build a probabilistic model of rotation and devise a matrix Fisher-based regressor for jointly predicting rotation along with its prediction uncertainty. We then propose to use the entropy of the predicted distribution as a confidence measure, which enables us to perform pseudo label filtering for rotation regression. For supervising such distribution-like pseudo labels, we further investigate the problem of how to enforce loss between two matrix Fisher distributions. Our extensive experiments show that our method can work well even under very low labeled data ratios on different benchmarks, achieving significant and consistent performance improvement over supervised learning and other semi-supervised learning baselines. Our project page is at https://yd-yin.github.io/FisherMatch.