Lexical Definition

‎χειροτονέω‎ cheirotonéō (khi-rot-on-eh'-o) to appoint ^G:V
from a comparative of ‎χείρ‎ and (to stretch)

choose, ordain.

• to be a hand-reacher or voter (by raising the hand), i.e. (generally) to select or appoint

Abbott-Smith

* χειρο-τονέω, -ῶ (< χείρ, τείνω)
1. to vote by stretching out the hand in the Athenian ἐκκλησία (Luc., Plut.).
2. to appoint:
(a) by vote, II Co 8:19
(b) without vote, Ac 14:23 (v. Rackham, in l.) (cf. προχειροτονέω).†

Abbott-Smith References

Liddell-Scott-Jones

χειροτονέω-έω,

stretch out the hand, for the purpose of giving one's vote in the assembly, περὶ τῶν ἀνδρῶν [Refs 1st c.AD+]; μὴ χ. vote against the motion, [Refs 2nd c.AD+] —but mostly,

__II with accusative person, elect, properly by show of hands, [Refs 5th c.BC+]:—passive, to be elected, [Refs 5th c.BC+]; ἐπὶ τοῦτ᾽ ἐχειροτονέωήθησαν, ἵνα.. [Refs 5th c.BC+]; χ. ἐπὶ τῆς διοικήσεως Decrees cited in [χειροτονέωηθεὶς ἢ λαχών 5th-6th c.BC: Plato Philosophus “Politicus” 300a, compare 4th c.BC: Aeschines Orator 1.106. ">Refs 5th c.BC+]
__II.b later, generally, appoint, [Refs 1st c.AD+]; of the Jewish High Priest, [χειροτονέωημένον βασιλέα [prev. work] 6.13.9, compare 7.9.3 ">Refs 1st c.AD+]; appoint to an office in the Church, πρεσβυτέρους [NT]
__II.2 with accusative of things, vote for a thing, [Refs 5th c.BC+]infinitive, ὁ δῆμος ἐχειροτόνησεν ἐξεῖναι.. πέμπειν voted to send, [Refs 4th c.BC+] —passive, κεχειροτόνηται ὕβρις τὸ πρᾶγυ᾽ εἶναι it is voted, ruled to be.., [Refs 4th c.BC+]
__III span with the hand, τὸ αἰδοῖον [Refs 2nd c.AD+]; χειροκοπεῖν codices).

_{LSJ Scripture Refs: Acts.14.23 ☩ 2Cor.8.19}