Yes, he did. He was asked with which weapons the third world war would be fought. He answered - in German - with the following remark:
Ich bin [mir] nicht sicher, mit welchen Waffen der dritte Weltkrieg ausgetragen wird, aber im vierten Weltkrieg werden sie mit Stöcken und Steinen kämpfen
(from Calaprice, Alice (2005). The new quotable Einstein. Princeton University Press. p. 173. ISBN 0-691-12075-7)
Which translated means something like
I am not sure with which weapons the third world war will be fought, but in the fourth world war they will fight with sticks and stones.
So depending on how much artistic freedom you want to give the translators, yes, he did say that.
Partial image of page 173 of Calaprice's book from Amazon: