The aim of this work was to optimize spot welding of unidirectional tapes made of polycarbonate and carbon fibers. Three studies were performed to investigate the influences of various welding conditions on the quality of the welded spot. First, we used a full factorial experimental design to analyze the influence of temperature and time on the welds’ tensile stress at break. Second, we repeated the experiment with optimized settings and conditions. Finally, we adopted a central composite design (CCD) to investigate the stability of the process. Our results show that temperature had the greatest influence on weld quality. The maximum tensile stress achieved was 23 MPa. Using a relatively high temperature for a short welding time resulted in self-cleaning of the welding head and in a faster and more stable process, and gel permeation chromatography (GPC) confirmed that these conditions caused no additional degradation.