The complex environment and chaotic stacking of parts at manufacturing sites in aerospace, automotive, and other fields, result in low registration accuracy of acquiring 3D point cloud data. This paper proposes a robust point cloud registration method that combines the sampling consensus initial with the threshold-based fine registration algorithm, establishes the point-to-face error metric function, and accomplishes accurate registration in the case of low overlap between the measured point cloud and the template point cloud. A comparison of the registration experiments conducted with this paper’s method with existing methods revealed that the RMS distance error and angular error were optimized by 94.2% and 83.4%, respectively, on average. Furthermore, the target recognition accuracy for automatic robot grasping was found to be 95%. The point cloud registration method presented in this paper exhibited high alignment accuracy and robustness, and was able to provide accurate target part position for automatic robot gripping.