This is either a spelling or a pronunciation anomaly; I'm not sure which. Why is "eye" pronounced as the letter "I"?
Looking at the Etymonline entry:
c.1200, from O.E. ege (Mercian), eage (W. Saxon), from P.Gmc. *augon
the g in Old English ege would be the voiced velar fricative /ɣ/. This sound does not exist in modern English as it was palatalised to /ʝ/ and later became /j/, which we usually write with y.
Both spelling and pronunciation are reasonably regular. The word is from Mercian ēge [e:ɣe] (West Saxon ēage). In Middle English the [ɣ] became [j], and the combination [e:j] developed into the diphthong [eɪ]. In later Middle English this diphthong was monophthongized to [i:], which developed into modern [aɪ] in the course of the Great Vowel Shift. The later Middle English pronunciation can be seen in such spellings as igh(e), ihe, and ie; the modern spelling, however, represents the earlier Middle English pronunciation.