Eye tracking techniques based on deep learning are rapidly spreading in a wide variety of application fields. With this study, we want to exploit the potentiality of eye tracking techniques in ocular proton therapy (OPT) applications. We implemented a fully automatic approach based on two-stage convolutional neural networks (CNNs): the first stage roughly identifies the eye position and the second one performs a fine iris and pupil detection. We selected 707 video frames recorded during clinical operations during OPT treatments performed at our institute. 650 frames were used for training and 57 for a blind test. The estimations of iris and pupil were evaluated against the manual labelled contours delineated by a clinical operator. For iris and pupil predictions, Dice coefficient (median = 0.94 and 0.97), Szymkiewicz–Simpson coefficient (median = 0.97 and 0.98), Intersection over Union coefficient (median = 0.88 and 0.94) and Hausdorff distance (median = 11.6 and 5.0 (pixels)) were quantified. Iris and pupil regions were found to be comparable to the manually labelled ground truths. Our proposed framework could provide an automatic approach to quantitatively evaluating pupil and iris misalignments, and it could be used as an additional support tool for clinical activity, without impacting in any way with the consolidated routine.