In this paper we propose a method for matching the scales of 3D point clouds. 3D point sets of the same scene obtained by 3D reconstruction techniques usually differ in scale. To match scales, we estimate the ratio of scales of two given 3D point clouds. By performing PCA of spin images over different scales of two point clouds, two sets of cumulative contribution rate curves are generated. Such sets of curves can be considered to characterize the scale of the given 3D point clouds. To find the scale ratio of two point clouds, we register the two sets of curves by using a variant of ICP that estimates the ratio of scales. Simulations with the Stanford bunny and experimental results with 3D reconstructions of artificial and real scenes demonstrate that the ratio of any 3D point clouds can be effectively used for scale matching.