To solve the registration problem of a three-dimensional (3D) point cloud under disorder, data occlusion and noise disturbance, a scale point cloud registration algorithm in high-dimensional orthogonal subspace mapping is proposed. The point cloud to be registered is scaled up to complete the affine registration according to the energy-power ratio. The registration accuracy of the proposed algorithm is comparable to that of the classical iterative closest point (ICP)algorithm when the point cloud is out of order with data occluded, size scaled and noise disturbance. Compared with the classical ICP algorithm, the proposed algorithm improves the registration efficiency of the Bunny point cloud data by 98% and the registration speed of the Dragon point cloud data by at least 20 times. Moreover, in the registration of the large-scale Dragon point cloud data, the registration time of the proposed algorithm is 6210.4 s less than that of the classical ICP algorithm, and the registration accuracy is higher than those of other algorithms. The proposed algorithm does not fall into the local minimum and possesses obvious advantages in terms of fast and accurate registration and stability.