It is shown that a massive Abelian vector boson field can generate the curvature perturbation in the Universe, when coupled non-minimally to gravity, through an RA2 coupling. The vector boson acts as a curvaton field imposing the curvature perturbation after the end of inflation, without generating a large-scale anisotropy. The parameter space of the model is fully explored, obtaining the relevant bounds on the inflation scale and the decay constant of the vector curvaton.