We give a construction to obtain canonically an isotropic average of given $C^1$-close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein's submanifold averaging theorem and apply Moser's trick. We show some applications to the existence of invariant isotropic submanifolds under group actions, to images of isotropic submanifolds under moment maps, and to contact geometry.