Plasma rotational velocity measurements may be applied to the test of plasma theory, to the assessment of the effects of plasma perturbations, and as substitutes for electric field measurements. For these applications, we developed a plasma rotation diagnostic based on the measurement of the Doppler shift of impurity spectra. In ohmic plasmas, the measurement is complicated by the small size of the velocity induced line shift compared with the line width. To overcome this problem, our diagnostic system is configured to observe each of two plasma regions at several times during a single shot using a single array detector. This procedure can eliminate the need for a separate absolute wavelength calibration if the regions are properly chosen and can minimize the effects of detector noise and shot-to-shot plasma variation. The two chords selected for observation can be changed from shot to shot. The details of the novel optical system are described. As an example of the technique, rotational velocity profiles for ohmic plasmas perturbed by a radial, resonant magnetic field are presented.