oracle n.

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).

"of or pertaining to, or of the nature of, an oracle or oracles," 1670s, from Latin oraculum (see oracle) + -ar. The older word was oraculous (1610s). Related: Oracularity.