A much-reprinted theory that the word comes from one of the various derivatives from Nahuatl xote- "lame" (e.g., xotemol "limping," xotepol 'id.,' etc...) is unpersuasive. The semantic shift between "lame" and vulture" is a stretch, and the geography is all wrong; there is no explanation why a Nahuatl word ended up in the dialects of southernmost Spanish. Another theory, that jote comes from Nahuatl xotlapech, some type of bird of yellow and blue feathers, suffers from the same problems and is phonologically less attractive. See Lenz (1904).
Two later etymologies of the word may be safely discarded as well without further comment: one, that the word is an "abbreviation" of aligote; and two, that the word comes from grajote. See Román (1908).