mid-14c. (transitive), from Old French enroller "record in a register, write in a roll" (13c., Modern French enrôler), from en- "make, put in" (see en- (1)) + rolle (see roll (n.)). Related: Enrolled; enrolling.
word-forming element meaning "in; into," from French and Old French en-, from Latin in- "in, into" (from PIE root *en "in"). Typically assimilated before -p-, -b-, -m-, -l-, and -r-. Latin in- became en- in French, Spanish, Portuguese, but remained in- in Italian.
Also used with native and imported elements to form verbs from nouns and adjectives, with a sense "put in or on" (encircle), also "cause to be, make into" (endear), and used as an intensive (enclose). Spelling variants in French that were brought over into Middle English account for parallels such as ensure/insure, and most en- words in English had at one time or another a variant in in-, and vice versa.
c. 1200, rolle, "rolled-up piece of parchment or paper, scroll" (especially one inscribed with an official record), from Old French rolle "document, parchment scroll, decree" (12c.), Medieval Latin rotulus "a roll of paper" (source also of Spanish rollo, Italian rullo), from Latin rotula "small wheel," diminutive of rota "wheel" (see rotary). Dutch rol, German Rolle, Danish rulle, etc. are from French.
The meaning "a register, a list, a catalogue" is from late 14c., common from c. 1800. The general sense of "quantity of material rolled up" also is from late 14c. Specific cookery meaning "small quantity of dough which is rolled before baking" is recorded from mid-15c. The meaning "quantity of paper money" is from 1846; the sense of "quantity of (rolled) film" is from 1890.