I will talk about some applications of the Witt vector cohomology to the 3-dimensional minimal model theory of positive characteristic. We show that klt threefolds, whose characteristic are larger than 5, have Witt rational singularities (the Witt version of rational singularities). Using this, we prove that a klt Fano threefold over a finite field contains a rational point. This is a joint work with Y. Gongyo and Y. Nakamura.