Three-dimensional (3D) modeling for the documentation, preservation, and management of cultural heritage is indispensable. To achieve this goal, a low-cost unmanned aerial vehicle (UAV) combined with the Structure from Motion (SfM) photogrammetric technique was utilized to build a 3D model and conduct surface crack measurements of cultural monuments. The results showed that, under simple conditions, non-specialists can easily generate accurate 3D models from UAV-acquired imagery. In this study, the statistical errors of checkpoints between 3D reconstruction and field measurements, expressed as total RMSE, ranged from 0.103 m to 0.848 m. However, the mean absolute errors of surface crack measurements between tape-based methods and 3D reconstruction ranged from 0.002 m to 0.099 m. Furthermore, UAV-SfM was applied to measure surface crack lengths on an inaccessible cultural monument. The findings demonstrated that employing the UAV-SfM photogrammetric technique for 3D reconstruction of cultural monuments is both feasible and reliable.