A highly efficient phase shifter based on the silicon-organic hybrid (SOH) platform is theoretically investigated and experimentally tested. The device consists of a silicon slot waveguide covered with an organic liquid-crystal (LC) cladding. A record-low voltage-length product of U(π)L = 0.085 Vmm can be achieved for high-purity materials where an optimum operation point can be set by a DC bias. With standard materials and without a DC bias, we measure a phase shift of 35π with a drive voltage of only 5 V for a 1.7 mm long device corresponding to a voltage-length product of U(π)L = 0.24 Vmm. The power dissipation is about six orders of magnitude smaller than that of state-of-the-art thermo-optic devices, thereby enabling dense integration of LC phase shifters in advanced photonic integrated circuits.