We use daily full-disk vector magnetograms from Vector Spectromagnetograph on Synoptic Optical Long-term Investigations of the Sun system to synthesize the first Carrington maps of the photospheric vector magnetic field. We describe these maps and make a comparison of the observed radial field with the radial field estimate from line-of-sight magnetograms. Furthermore, we employ these maps to study the hemispheric pattern of current helicity density, H-c, during the rising phase of solar cycle 24. The longitudinal average over the 23 consecutive solar rotations shows a clear signature of the hemispheric helicity rule, i.e., H-c is predominantly negative in the north and positive in the south. Although our data include the early phase of cycle 24, there appears to be no evidence for a possible (systematic) reversal of the hemispheric helicity rule at the beginning of the cycle as predicted by some dynamo models. Furthermore, we compute the hemispheric pattern in active region latitudes (-30 degrees <= theta <= 30 degrees) separately for weak (100G < vertical bar B-r vertical bar < 500 G) and strong (vertical bar B-r vertical bar > 1000 G) radial magnetic fields. We find that while the current helicity of strong fields follows the well-known hemispheric rule (i.e., 0 . H-c < 0), H-c of weak fields exhibits an inverse hemispheric behavior (i.e., theta . H-c > 0), albeit with large statistical scatter. We discuss two plausible scenarios to explain the opposite hemispheric trend of helicity in weak and strong field regions.