In this study, laser-assisted machining experiments are carried out on silicon carbide (SiC) ceramic materials by a turning process, and laser power, cutting depth, rotational speed, and feed speed are selected as research factors. In order to improve the surface processing quality of laser-assisted turning of SiC ceramics and obtain the smallest surface roughness, the orthogonal method and response surface method are used to investigate the effect of various factors on surface roughness. The effect of various factors on surface roughness is evaluated by variance analysis, mean analysis, main effect diagram, 3D response surface, and corresponding contour diagram. The surface roughness prediction model is established based on the response surface method, and the prediction error is 4.1% with high accuracy. The experimental results show that laser power and cutting depth are the most significant factors affecting surface roughness, and rotational speed is a significant factor affecting surface roughness. Under the optimum process conditions, the smallest surface roughness Ra obtained by the response surface method is 0.294 μm, which is lower than 0.315 μm obtained by the orthogonal method, and the surface quality is higher. Therefore, the optimal process parameters of the response surface method can obtain the smallest surface roughness and higher surface quality in laser-assisted turning of SiC ceramics.