The design and construction of a superconducting magnet system, producing a maximum magnetic field of 0.6 T with any desired direction, is described. The magnet consists of a pair of Helmholtz coils, which can be rotated about a fixed solenoid. The azimuthal angle of the field is selected manually by rotation of the Helmholtz coils, and the polar angle is selected electronically by adjusting the currents in the Helmholtz coils and solenoid appropriately. The latter is accomplished automatically by means of the associated power supply, which is described in detail. The accuracy of the magnet system is approximately 0.8 mT or ½% of the field magnitude, whichever is greater. This system has proved to be indispensable for studies of the rf size effect in pure metals at low temperatures. temperatures.