As the sheep industry rapidly moves towards modernization, digitization, and intelligence, there is a need to build breeding farms integrated with big data. By collecting individual information on sheep, precision breeding can be conducted to improve breeding efficiency, reduce costs, and promote healthy breeding practices. In this context, the accurate identification of individual sheep is essential for establishing digitized sheep farms and precision animal husbandry. Currently, scholars utilize deep learning technology to construct recognition models, learning the biological features of sheep faces to achieve accurate identification. However, existing research methods are limited to pattern recognition at the image level, leading to a lack of diversity in recognition methods. Therefore, this study focuses on the small-tailed Han sheep and develops a sheep face recognition method based on three-dimensional reconstruction technology and feature point matching, aiming to enrich the theoretical research of sheep face recognition technology. The specific recognition approach is as follows: full-angle sheep face images of experimental sheep are collected, and corresponding three-dimensional sheep face models are generated using three-dimensional reconstruction technology, further obtaining three-dimensional sheep face images from three different perspectives. Additionally, this study developed a sheep face orientation recognition algorithm called the sheep face orientation recognition algorithm (SFORA). The SFORA incorporates the ECA mechanism to further enhance recognition performance. Ultimately, the SFORA has a model size of only 5.3 MB, with accuracy and F1 score reaching 99.6% and 99.5%, respectively. During the recognition task, the SFORA is first used for sheep face orientation recognition, followed by matching the recognition image with the corresponding three-dimensional sheep face image based on the established SuperGlue feature-matching algorithm, ultimately outputting the recognition result. Experimental results indicate that when the confidence threshold is set to 0.4, SuperGlue achieves the best matching performance, with matching accuracies for the front, left, and right faces reaching 96.0%, 94.2%, and 96.3%, respectively. This study enriches the theoretical research on sheep face recognition technology and provides technical support.