Three-dimensional reconstruction is a common method for cultural relics information conservation, mainly through point cloud alignment technology to reorganize the spatial point cloud information of cultural relics, and its alignment accuracy has an important impact on cultural relics recovery. To address the problems of low accuracy and poor robustness in the alignment of complex point cloud texture features on the surface of cultural relics, this paper proposes a local point cloud alignment method based on normal vector angle and faceted index features. Firstly, the normal vector angle and covariance matrix thresholds are set according to the point cloud planar characteristics, and the point cloud feature points satisfying both features are extracted; secondly, the point cloud local feature point set is extracted by the K-nearest neighbor search methhod, and the two sets of point cloud center-of-mass positions are overlapped by rigid transformation for coarse alignment; finally, the nearest points are iterated based on ICP for fine alignment. By comparing with the traditional ICP, the point cloud alignment error of the proposed method reduces by 3% and the matching time reduces by 50%, which effectively improves the accuracy and efficiency of alignment and enhances the robustness of point cloud alignment.