An important component in digital circuits is a phase rotator, which permits precise time-shifting (or equivalently, phase rotation) of a clock signal within a clock period. A digital phase rotator can access multiple discrete values of phase under digital control. Such a device can have application in digital clock synchronization circuits, and can also be used for a digital phase modulator that encodes a digital signal. A digital phase rotator has been implemented in superconducting integrated circuit technology, using rapid single-flux-quantum logic (RSFQ). This circuit can exhibit positive or negative phase shifts of a multi-phase clock. Arbitrary precision can be obtained by cascading a plurality of phase rotator stages. Such a circuit forms a phase-modulator that is the core of a direct digital synthesizer that can operate at multi-gigahertz radio frequencies.