Torsional eye movements are rotations of the eye around the line of sight. Measuring torsion is essential to understanding how the brain controls eye position and how it creates a veridical perception of object orientation in three dimensions. Torsion is also important for diagnosis of many vestibular, neurological, and ophthalmological disorders. Currently, there are multiple devices and methods that produce reliable measurements of horizontal and vertical eye movements. Measuring torsion, however, noninvasively and reliably has been a longstanding challenge, with previous methods lacking real-time capabilities or suffering from intrusive artifacts. We propose a novel method for measuring eye movements in three dimensions using modern computer vision software (OpenCV) and concepts of iris recognition. To measure torsion, we use template matching of the entire iris and automatically account for occlusion of the iris and pupil by the eyelids. The current setup operates binocularly at 100 Hz with noise< 0.1 and is accurate within 20 of gaze to the left, to the right, and up and 10 of gaze down. This new method can be widely applicable and fill a gap in many scientific and clinical disciplines.