We investigate optical second harmonic generation (SHG) from individual self-catalyzed zinc-blende (ZB) GaAs nanowires (NWs), where the polarimetry strongly depends on the NW diameter. We report a direct observation on the SHG induced by surface nonlinear susceptibilities in a single, ultra-thin GaAs NW. By considering the contributions from both optical field and structural discontinuities in our theoretical model, we can well explain the optical SHG polarimetry from NWs with different diameters. We also show that the optical in-coupling coefficient arising from the depolarization electromagnetic field can determine the polarization of the SHG. The results open perspectives for further geometry-based studies on the origin and control of SHG in small nanostructures.