We demonstrate for the first time a waveguide-based frequency shifter on the silicon photonic platform using single-sideband modulation. The device is based on silicon-organic hybrid (SOH) electro-optic modulators, which combine conventional silicon-on-insulator waveguides with highly efficient electro-optic cladding materials. Using small-signal modulation, we demonstrate frequency shifts of up to 10 GHz. We further show large-signal modulation with optimized waveforms, enabling a conversion efficiency of -5.8 dB while suppressing spurious side-modes by more than 23 dB. In contrast to conventional acousto-optic frequency shifters, our devices lend themselves to large-scale integration on silicon substrates, while enabling frequency shifts that are several orders of magnitude larger than those demonstrated with all-silicon serrodyne devices.