When a visual stimulus oscillates in luminance, pupil size follows this oscillation. Recently, it has been demonstrated that such induced pupil oscillations can be used to tag which stimulus is covertly attended. Here we ask whether this “pupil frequency tagging” approach can be extended to visual awareness, specifically to inferring perceptual dominance in Binocular Rivalry between complex stimuli. We presented two distinct stimuli, a face and a house, to each eye and modulated their luminance at 1.7 Hz either in counter-phase (180° phase shift), with a 90° phase shift or in phase (0° control). In some conditions, we additionally asked observers to attend either of the stimuli. The luminance modulation was sufficiently subtle that rivalry dynamics did not differ among these conditions, and was also indistinguishable from unmodulated presentation of the stimuli. For the 180° and the 90° phase-shifted stimuli, we found that the phase of the pupil response relative to the stimuli was modulated by perceptual dominance; that is, the relative phase depended on the stimulus the observer was aware of. In turn, this perceptually dominant stimulus could be decoded from the phase of the pupil response significantly above chance. Neither percept dependence of the phase nor significant decoding was found for the 0° control condition. Our results show that visual awareness modulates pupil responses and provide proof of principle that dominance in rivalry for complex stimuli can be inferred from induced pupil fluctuations.