"a part of an army expressly organized and having a head," 1704, from French corps d'armée (16c.), which apparently was picked up in English during Marlborough's campaigns, from French corps (old French cors) "body," from Latin corpus "body" (from PIE root *kwrep- "body, form, appearance"); see corpse, which is a doublet of this word, for the pronunciation.
The field corps, a tactical unit of a large army composed of two or more divisions, began with Napoleon. The word was extended to other organized groups under a leader, as in corps de ballet (1826), corps diplomatique (1796). Corpsman "enlisted medical auxiliary in the U.S. military" is from 1941.