1530s, varment; the chiefly American English dialectal form varmint is attested from 1829; colloquial variant of vermin. Meaning "objectionable or troublesome person" is recorded from 1773.
Entries linking to varmint
vermin n.
c. 1300, "noxious animals," from Anglo-French and Old French vermin "moth, worm, mite," in plural "troublesome creatures" (12c.), from Vulgar Latin *verminum "vermin," possibly including bothersome insects, collective noun formed from Latin vermis "worm" (from PIE root *wer- (2) "to turn, bend"). Extended to "low, obnoxious people" by 1560s.