1560s, "one who dodges or evades" in any sense, especially "one practiced in artful shifts," agent noun from the literal or figurative (especially underworld) senses of dodge (v.).
The U.S. meaning "corn cake" is recorded from 1831 (usually as corn-dodger) and is perhaps a different word: Compare Northern English dialectal dodge "lump, large piece" (1560s).
The Artful Dodger (Jack Dawkins), so called for his skill in picking pockets, leader of a gang of child criminals, is from Dickens' "Oliver Twist" (1837-39).
The U.S. baseball club the Dodgers, originally based in Brooklyn, N.Y., was so called from 1900, from trolley dodgers, a Manhattanites' nickname for Brooklyn residents, in reference to the streetcar lines that then crisscrossed the borough.