We define gaze agency as the awareness of the causal effect of one's own eye movements in gaze-contingent environments, which might soon become a widespread reality with the diffusion of gaze-operated devices. Here we propose a method for measuring gaze agency based on self-monitoring propensity and sensitivity. In one task, naïf observers watched bouncing balls on a computer monitor with the goal of discovering the cause of concurrently presented beeps, which were generated in real-time by their saccades or by other events (Discovery Task). We manipulated observers' self-awareness by pre-exposing them to a condition in which beeps depended on gaze direction or by focusing their attention to their own eyes. These manipulations increased propensity to agency discovery. In a second task, which served to monitor agency sensitivity at the sensori-motor level, observers were explicitly asked to detect gaze agency (Detection Task). Both tasks turned out to be well suited to measure both increases and decreases of gaze agency. We did not find evident oculomotor correlates of agency discovery or detection. A strength of our approach is that it probes self-monitoring propensity-difficult to evaluate with traditional tasks based on bodily agency. In addition to putting a lens on this novel cognitive function, measuring gaze agency could reveal subtle self-awareness deficits in pathological conditions and during development.