Beam-bunch arrival time has been measured for the first time by operating superconducting cavities, normally part of the linac accelerator array, in a bunch-detecting mode. The very high Q of the superconducting cavities provides high sensitivity and allows for phase-detecting low-current beams. In detecting mode, the resonator is operated at a very low field level comparable to the field induced by the bunched beam. Because of this, the rf field in the cavity is a superposition of a ''pure'' (or reference) rf and the beam-induced signal. A new method of circular phase rotation (CPR), allowing extraction of the beam phase information from the composite rf field was developed. Arrival time phase determination with CPR is better than 1 (at 48 MHz) for a beam current of 100 nA. The electronics design is described and experimental data are presented.