Discontinuity information is important in evaluating the security of a rock mass for the distribution of discontinuity spacings, which affects the mechanical properties and stability of the rock mass. Numerous studies have been conducted on the semi-automatic or automatic extraction of discontinuities from point cloud data. We developed a random sample consensus discontinuity detection (RANSAC) method to automatically extract discontinuities in a rock mass. The proposed method is entirely based on a raw point instead of a triangular mesh, which can retain the integrity of the data. A modified RANSAC algorithm is used to increase the degree of automation. The proposed approach consists of four steps: (1) calculation of the normal vector of the point cloud; (2) plane extraction using the modified RANSAC algorithm; (3) delineation of the boundary of the discontinuity using the modified Graham scan algorithm; and (4) calculation of the orientation and area on the basis of the normal vector and the boundary of the discontinuity. The results and the raw data source are freely provided for reproducible research and to develop the method further.