Elicit comes from Latin elicit- ‘drawn out by trickery or magic’, from the verb elicere, from e- (variant of ex- ) ‘out’ + lacere ‘entice, deceive’  to English in the early 17th century (1600s).  

According to the Oxford English Dictionary, the first known use of the word "elicit" in English was in the early 17th century, with the earliest recorded evidence appearing around 1624 in the writings of Francis White, bishop of Ely. 

Just the facts:

Elicit Definition & Meaning - Merriam-Webster