1630s, "soldier in a cavalry troop," from troop (n.) + -er (1). Extended to "mounted policeman" (1858, in Australia) then to "state policeman" (U.S.) by 1911.
Entries linking to trooper
troop n.
1540s, "body of soldiers," 1540s, from French troupe, from Old French trope "band of people, company, troop, crowd" (13c.), a word of uncertain origin, perhaps from Frankish *throp "assembly, gathering of people" or another Germanic source, perhaps related to Old English ðorp, Old Norse thorp "village" (see thorp). OED derives the French word from Latin troppus "flock," which is of unknown origin but also might be from the proposed Germanic source. Of groups of animals from 1580s. Specifically as "a subdivision of a cavalry force" from 1580s; of Boy Scouts from 1908. Troops "armed forces" is from 1590s.
-er 1
English agent noun ending, corresponding to Latin -or. In native words it represents Old English -ere (Old Northumbrian also -are) "man who has to do with," from Proto-Germanic *-ari (cognates: German -er, Swedish -are, Danish -ere), from Proto-Germanic *-arjoz. Some believe this root is identical with, and perhaps a borrowing of, Latin -arius (see -ary).
Generally used with native Germanic words. In words of Latin origin, verbs derived from past participle stems of Latin ones (including most verbs in -ate) usually take the Latin ending -or, as do Latin verbs that passed through French (such as governor); but there are many exceptions (eraser, laborer, promoter, deserter; sailor, bachelor), some of which were conformed from Latin to English in late Middle English.
The use of -or and -ee in legal language (such as lessor/lessee) to distinguish actors and recipients of action has given the -or ending a tinge of professionalism, and this makes it useful in doubling words that have a professional and a non-professional sense (such as advisor/adviser, conductor/conducter, incubator/incubater, elevator/elevater).