Let X be a smooth projective variety defined over a finite field. The Tate conjecture predicts that the cycle class map from the Chow groups of X with rational coefficients to the l-adic étale cohomology groups is surjective. The integral version, which is known not to be true in general, investigates the similar question for integral coefficients. In this talk we will explain how to prove this integral version for codimension two cycles on a cubic fourfold. The strategy is very much inspired by the approach of Claire Voisin used in the context of the integral Hodge conjecture. This is a joint work with F. Charles.