  We study the effects of the CP-breaking topological $\theta$-term in the
large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f$ degenerate light
flavors. We first compute the ground state energy density, the topological
susceptibility and the masses of the lowest lying mesons, finding agreement
with expectations from the QCD chiral effective action. Then, focusing on the
$N_f=2$ case, we consider the baryonic sector and determine, to leading order
in the small $\theta$ regime, the related holographic instantonic soliton
solutions. We find that while the baryon spectrum does not receive ${\cal
O}(\theta)$ corrections, this is not the case for observables like the
electromagnetic form factor of the nucleons. In particular, it exhibits a
dipole term, which turns out to be vector-meson dominated. The resulting
neutron electric dipole moment, which is exactly the opposite as that of the
proton, is of the same order of magnitude of previous estimates in the
literature. Finally, we compute the CP-violating pion-nucleon coupling constant
${\bar g}_{\pi N N}$, finding that it is zero to leading order in the large
$N_c$ limit.
