Can anxiety cause someone to have visual distortions?

Yes: There is evidence that anxiety/fear is involved in the encoding and processing of perceptual information, including that from the visual senses. One example is that those with arachnophobia, evidently see the spiders that they encounter as larger than those without arachnophobia.

Sure can but: Tunnel vision occuring with high anxiety has been well-known for a long time and employment of relaxation techniques such as deep breathing can help even in extreme situations such as combat. But, thte question begs what kind of visual disturbance?. Cetrain types of migraines can precipitate emotional states such as anxiety and visual field cuts etc. If in doubt see your doc.