1540s, "one who or that which incites to action," agent noun from prompt (v.)). Earlier was promptator (mid-15c.), from Medieval Latin. Meaning "one who helps a speaker or reciter" is from 1590s; the specific theatrical sense is from c. 1600.

early 14c., rethorike, "the art of eloquence and persuasiveness in language, the art of using language to influence others," from Old French retorike, rethorique (Modern French rhétorique) and directly from Latin rhetorice, from Greek rhētorikētekhnē  "art of an orator," from rhētōr (genitive rhētoros) "speaker, master speaker, orator; artist of discourse; teacher of rhetoric," especially (in the Attic official language), "orator in public." This is related to rhesis "speech," rhema "word, phrase, verb," literally "that which is spoken" (from PIE *wre-tor-, from root *were- (3) "to speak;" see verb). Since classical times with a derogatory suggestion of "artificial oratory" as opposed to what is natural or unaffected, "ostentatious declamation."

late 14c., oratour, "an eloquent or skilled speaker; one who pleads or argues for a cause," from Anglo-French oratour (Modern French orateur) and directly from Latin orator "speaker," from ōrare "to speak, speak before a court or assembly, pray to, plead."

This is sometimes said to be  from PIE root *or- "to pronounce a ritual formula" (source also of Sanskrit aryanti "they praise," Homeric Greek are, Attic ara "prayer," Hittite ariya- "to ask the oracle," aruwai- "to revere, worship").  But according to de Vaan, the Latin word is rather from Proto-Italic *ōs- "mouth," from PIE *os- "mouth" (see oral). He writes:

The chronology of the attestations shows that 'to plead, speak openly' is the original meaning of orare .... The alternative etymology ... seems very unlikely to me: a connection with Skt. a-aryanti 'they acknowledge' and Ru. orat' 'to shout', since nothing suggests a meaning 'to shout' for the Latin verb, nor does it seem onomatopoeic.

The general meaning "public speaker," is attested from early 15c. Fem. forms were oratrice (early 15c., from Anglo-French); oratrix (mid-15c., from Latin); oratress (1580s).

German word for the jargon of thieves and vagabonds, 1841, from German Rotwelsch, literally "Red Welsh," from rot "red" (see red (adj.1)) + Welsh because (to a German-speaker) it would seem obscure and difficult. The first element rather might be connected with Middle High German rot "beggar."

word-forming element meaning "voice, sound," also "speaker of," from Greek phōnē "voice, sound" of a human or animal, also "tone, voice, pronunciation, speech," from PIE root *bha- (2) "to speak, say, tell" (source also of Latin for, fari "to speak," fama "talk, report").