We show that a Weyl law holds for the variational spectrum of the $p$-Laplacian. More precisely, let $(��_i)_{i=1}^\infty$ be the variational spectrum of $��_p$ on a closed Riemannian manifold $(X,g)$ and let $N(��) = \#\{i:\, ��_i < ��\}$ be the associated counting function. Then we have a Weyl law $N(��) \sim c \operatorname{vol}(X) ��^{n/p}$. This confirms a conjecture of Friedlander. The proof is based on ideas of Gromov and Liokumovich, Marques, Neves.