Yours, Etc.: Origins and Uses of 8 Sign-Offs
late 14c., in reference to ancient Rome, from Latin circus "ring, circular line," which was applied by Romans to circular arenas for performances and contests and oval courses for racing (especially the Circus Maximus), from or cognate with Greek kirkos "a circle, a ring," from PIE *kirk- from root *(s)ker- "to turn, bend" (see ring (n.)).
In reference to modern large arenas for performances from 1791; sense then extended to the performing company, hence "traveling show" (originally traveling circus, 1838). Extended in World War I to squadrons of military aircraft. Meaning "lively uproar, chaotic hubbub" is from 1869. Sense in Picadilly Circus and other place names is from early 18c. sense "buildings arranged in a ring," also "circular road." The adjective form is circensian.