Existing point cloud registration algorithms are not effective for cross-source point cloud registration. To address this issue, this paper proposes a cross-source point cloud registration algorithm that uses angle constraints. The algorithm redefines the weight coefficients of the fast point feature histogram (FPFH) algorithm to adapt it to point cloud data with different scales and improve the inlier rate of matching point pairs. Additionally, the algorithm uses angle constraints to filter the matching point pairs and reserves those with good compatibility to estimate scale, thus unifying the scale of two point clouds. In the coarse registration phase, the compatibility triangles satisfying the distance constraint are filtered to calculate the coarse registration matrix, thus completing the preliminary transformation. Finally, the iterative closest point (ICP) algorithm is used for fine registration to improve the overall registration accuracy. Experimental results show that the proposed algorithm has a good registration effect on point cloud data with same and different scales and can quickly register point clouds.