Point cloud registration is a fundamental element of the three-dimensional reconstruction processes. In this study, a point cloud registration algorithm is proposed based on the maximum sum of squares of the correlation coefficients (MCC) to address the issues of scattered point clouds, missing data, and low registration efficiency and accuracy under noise interference. Further, the target point cloud and the point cloud to be registered are de-averaged and rotated, so that the MCC between row vectors of the two sets of point clouds can be achieved after rotation. Subsequently, particle swarm optimization algorithm is used to derive two sets of intermediate-state rotation matrices. Finally, based on these matrix sets, the rotation matrix and translation vector between two point clouds are obtained for registering the point cloud. The simulation results show that the proposed algorithm is faster, more accurate, and more robust compared with the remaining existing algorithms when point clouds are scattered, missing, and interrupted by noise.