Point cloud registration (PCR) is a vital problem in remote sensing and computer vision, which has various important applications, such as 3D reconstruction, object recognition, and simultaneous localization and mapping (SLAM). Although scholars have investigated a variety of methods for PCR, the applications have been limited by low accuracy, high memory footprint, and slow speed, especially for dealing with a large number of point cloud data. To solve these problems, a novel local descriptor is proposed for efficient PCR. We formed a comprehensive description of local geometries with their statistical properties on a normal angle, dot product of query point normal and vector from the point to its neighborhood point, the distance between the query point and its neighborhood point, and curvature variation. Sub-features in descriptors were low-dimensional and computationally efficient. Moreover, we applied the optimized sample consensus (OSAC) algorithm to iteratively estimate the optimum transformation from point correspondences. OSAC is robust and practical for matching highly self-similar features. Experiments and comparisons with the commonly used descriptor were conducted on several synthetic datasets and our real scanned bridge data. The result of the simulation experiments showed that the rotation angle error was below 0.025° and the translation error was below 0.0035 m. The real dataset was terrestrial laser scanning (TLS) data of Sujiaba Bridge in Chongqing, China. The results showed the proposed descriptor successfully registered the practical TLS data with the smallest errors. The experiments demonstrate that the proposed method is fast with high alignment accuracy and achieves a better performance than previous commonly used methods.