Cite
late Middle English (in cite (sense 3 of the verb), originally with reference to a court of ecclesiastical law): from Old French citer, from Latin citare, from ciere, cire ‘to call’.
wiktionary
From Old French citer, from Latin citare(“to cause to move, excite, summon”), frequentative of ciēre(“to rouse, excite, call”).
From the first syllable of citation. Analogous to quote, from quotation.
etymonline
cite (v.)
mid-15c., "to summon, call upon officially," from Old French citer "to summon" (14c.), from Latin citare "to summon, urge, call; put in sudden motion, call forward; rouse, excite," frequentative of ciere "to move, set in motion, stir, rouse, call, invite" from PIE root *keie- "to set in motion, to move to and fro."
Sense of "call forth a passage of writing, quote the words of another" is first attested 1530s. Related: Cited; citing.