They gave their hand, i.e. they covenanted or swore by giving their hand; which was the usual gesture in those cases; of which see Leviticus 6:2 Ezekiel 17:18.
Related Commentaries of Ezra 10:19
Ezra 10:19
19 And they gave their hands that they would put away their wives; and being guilty, they offered a ram of the flock for their trespass.