In this paper, a project and implementation of the parallel RANSAC algorithm in CUDA architecture for point cloud registration are presented. At the beginning, a serial state of the art method with several heuristic improvements from the literature compared to basic RANSAC is introduced. Subsequently, its algorithmic parallelization and CUDA implementation details are discussed. The comparative test has proven a significant program execution acceleration. The result is finding of the local coordinate system of the object in the scene in the near realtime conditions. The source code is shared on the Internet as a part of the Heuros system.