Green’s Dictionary of Slang

1. a person with very short hair.

c.1698		B.E. Dict. Canting Crew.
1725		New Canting Dict.
1791		W. Reeve ‘Tippy Bob’ song in Bluebeard [pantomime] I am sure I’m the thing, / Nay I wish I may swing, / If I an’t now a nice natty crop.
1797		Sporting Mag. Mar. IX 348/2: An old country squaretoes, to fopp’ry a foe, / And disgusted alike at a crop and a beau.

2. a Presbyterian [the severely cropped haircut favoured by the sect].

c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Crop. A Nick name for a Presbyterian: from their Cropping their Hair, which they trimmed close to a Bowl Dish, placed no their Heads; whence they were likewise termed Roundheads.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn).
1811		Lex. Balatronicum.