Friction Stir Welding (FSW) is a solid-state joining process for metals, non-metals and polymers. It is carried out with the help of a specially designed, non-consumable tool. The heat required, for creating a softened region at the faying surfaces, is generated by rotation of tool against the work piece material. Being a solid-state welding process, it offers several advantages like inducing minimum effect on the mechanical properties of base material, reduced shrinkage and distortion, no spatter or Ultra Violet (UV) radiations etc. However, developing a sound weld requires an appropriate combination of several process parameters e.g. the design of tool, its rotational and traversing speeds etc. To substantiate this aspect, an approach based on Response Surface Methodology (RSM) is presented during this paper that optimizes the combination of process parameters while investigating their effect on the mechanical properties of a friction stir welded butt joint configuration of Polycarbonate. To minimize the total number of combinations a Central Composite Rotatable Design (CCRD) is used with three factors and two levels. The results have shown that the butt joints fabricated at a traverse speed of 14 mm/min, rotational speed of 1700 RPM and with simple cylindrical conical tool geometry yielded the maximum ultimate tensile strength of 51.299 MPa.