Eye movements are disrupted in many neurodegenerative diseases and are frequent and early features in conditions affecting the cerebellum. Characterizing eye movements is important for diagnosis and may be useful for tracking disease progression and response to therapies. Assessments are limited as they require an in-person evaluation by a neurology subspecialist or specialized and expensive equipment. We tested the hypothesis that important eye movement abnormalities in cerebellar disorders (i.e., ataxias) could be captured from iPhone video. Videos of the face were collected from individuals with ataxia (n = 102) and from a comparative population (Parkinson's disease or healthy participants, n = 61). Computer vision algorithms were used to track the position of the eye which was transformed into high temporal resolution spectral features. Machine learning models trained on eye movement features were able to identify abnormalities in smooth pursuit (a key eye behavior) and accurately distinguish individuals with abnormal pursuit from controls (sensitivity = 0.84, specificity = 0.77). A novel machine learning approach generated severity estimates that correlated well with the clinician scores. We demonstrate the feasibility of capturing eye movement information using an inexpensive and widely accessible technology. This may be a useful approach for disease screening and for measuring severity in clinical trials.