"staff of office peculiar to royalty or independent sovereignty," c. 1300, ceptre, from Old French ceptre, sceptre (12c.) and directly from Latin sceptrum "royal staff," from Greek skēptron "staff to lean on," in a Persian and Asian context, "royal scepter," in transferred use, "royalty," from root of skeptein "'to support oneself, lean; pretend something, use as a pretention." Beekes has this from a root *skap- (perhaps non-Indo-European) and compares Latin scapus "shaft, stalk," Albanian shkop "stick, scepter," Old High German skaft, Old Norse skapt, Old English sceaft "shaft, spear, lance" (see shaft (n.1)).
The verb meaning "to furnish with a scepter" is from 1520s; hence "invest with royal authority." Related: Sceptred.