The detection of eye torsion is an important element for diagnosis of balance disorders, although it is rarely available in existing eye tracking systems. A novel method is proposed in this paper to provide robust measurement of torsional eye movements. A numerical approach is presented to estimate the iris boundary only according to the gaze direction, so the segmentation of the iris is more robust against occlusions and ambiguities. The perspective distortion of the iris pattern at eccentric eye positions is also corrected, benefiting from the transformation relation that is established for the iris estimation. The angle of the eye torsion is next measured on the unrolled iris patterns via a TM (Template Matching) technique. The principle of the proposed method is validated and its robustness in practice is assessed. A very low mean FPR (False Positive Rate) is reported (i.e., 3.3%) in a gaze test when testing on five participants with very different eye morphologies. The present method always gave correct measurement on the iris patterns with simulated eye torsions and rarely provided mistaken detections in the absence of eye torsion in practical conditions. Therefore, it shows a good potential to be further applied in medical applications.