c. 1300, "figure of a circle, a plane figure whose periphery is everywhere equidistant from its center point," from Old French cercle "circle, ring (for the finger); hoop of a helmet or barrel" (12c.), from Latin circulus "circular figure; small ring, hoop; circular orbit" (also source of Italian cerchio), diminutive of circus "ring" (see circus).
Replaced Old English trendel and hring. Late Old English used circul, from Latin, but only in an astronomical sense. Also used of things felt to be analogous to a circle: The meaning "group of persons surrounding a center of interest" is from 1714 (it also was a secondary sense of Latin circulus); that of "coterie" is from 1640s (a sense also found in Latin circulus).
To come full circle is in Shakespeare. Sense in logic, "inconclusive argument in which unproved statements are used to prove each other" is from 1640s. Meaning "dark mark around or beneath the eyes" is from 1848.