  We compute the electric dipole moment of nucleons in the large $N_c$ QCD
model by Witten, Sakai and Sugimoto with $N_f=2$ degenerate massive flavors.
Baryons in the model are instantonic solitons of an effective five-dimensional
action describing the whole tower of mesonic fields. We find that the dipole
electromagnetic form factor of the nucleons, induced by a finite topological
$\theta$ angle, exhibits complete vector meson dominance. We are able to
evaluate the contribution of each vector meson to the final result - a small
number of modes are relevant to obtain an accurate estimate. Extrapolating the
model parameters to real QCD data, the neutron electric dipole moment is
evaluated to be $d_n = 1.8 \cdot 10^{-16}\, \theta\;e\cdot \mathrm{cm}$. The
electric dipole moment of the proton is exactly the opposite.
