We create exciton-polariton condensates in half-moon shapes by the nonresonant optical excitation of GaAs-based cylindrical pillar microcavities. In this geometry, the π-jump of the phase of the condensate wave function coexists with a gradual ±πphase variation between two horns of the half-moon. We switch between clockwise and counterclockwise phase currents by slightly shifting the excitation spot on the surface of the pillar. Half-moon condensates are expected to reveal features of two-level quantum systems similar to superconducting flux qubits.