Aiming at the problems that the traditional spatial arc fitting method has poor robustness and low fitting accuracy, a robust spatial arc fitting optimization method is proposed. Firstly, on the basis of Lagrangian multiplier method, the objective function was established based on the constraint of the plane condition, and then the spatial arc fitting equation was derived. Secondly, the error tracking point was eliminated by using the RANSAC (random sample consensus) algorithm, which applied the high stability of RANSAC to the point cloud optimization of spatial arc fitting to improve the fitting accuracy. Finally, the feasibility of the proposed spatial arc fitting optimization method was verified by experimental analysis, and the fitting accuracy of the proposed method was analyzed through comparing with the traditional fitting method. The experimental results showed that the relative accuracy of ordinary arc point cloud fitting was about 0.003, and the relative accuracy of complex arc point cloud fitting was about 0.01. Compared with the traditional fitting method, the proposed method effectively solved the problems of low fitting accuracy and poor robustness. The research results indicate that the proposed spatial arc fitting optimization method can enhance robustness by using Lagrange multiplier method and improve fitting accuracy by using RANSAC algorithm to eliminate the error points, which has a wide range of practical engineering application.