The friction stir spot welding (FSSW) process is one of the main solid-state joining methods used widely for welding different materials and dissimilar metals. In this article, the welding of Polytetrafluoroethylene (PTFE) and aluminum alloy sheets by the FSSW process will be investigated experimentally. The joining of polymer (PTFE) and metal (AA1050 aluminum alloy) was done successfully. The effect of process parameters including tool rotational speed, penetration depth, initial holding time, dwell time, and tool shoulder diameter on the joint strength and elongation of the weldments will be studied using response surface methodology (RSM). The joint strength was increased by creating a threaded hole in the aluminum sheet. A mechanical lock was created between the softened PTFE and the edge of the threaded hole. The shear-tensile tests have been carried out for 32 designed experiments. The results show that the joint strength increased by increasing the initial holding time due to the better wettability of PTFE and aluminum sheet. The joint strength increased by increasing the tool rotational speed and tool diameter (better pouring of the hole and formation of the mechanical lock). Two different fracture modes have been observed in the samples: (1) fracture in the peripheral area of the joint (partial interfacial fracture mode) and (2) fracture in the mechanically locked area (pull-out mode with tearing).