Friction stir welding (FSW), a solid-state joining process, has gained significant attention for its ability to enhance weld quality and mechanical properties. This study optimizes the FSW parameters for AZ31C magnesium alloy reinforced with silicon carbide (SiCp) nanoparticles using a hybrid grey relational analysis—technique for order preference by similarity to ideal solution (GRA-TOPSIS) approach. The effects of SiCp content (5 wt%), tool tilt angle (1°, 1.5°, and 2°), rotational speed (1000, 1500, and 2000 rpm), tool profile (threaded, cylindrical, and conical), and traverse speed (5, 10, and 16 mm/min) were analyzed. The results indicate that the optimal welding parameters—rotational speed of 2000 rpm, traverse speed of 10 mm/min, tilt angle of 1.5°, and a conical tool profile—significantly enhanced mechanical performance. The highest tensile strength (274 MPa), microhardness (102 HV), and impact strength (109 MPa) were achieved under these conditions, demonstrating the effectiveness of SiCp reinforcement and process optimization.