Recent dynamical studies indicate that the possibility of an Earth-like planet around α Cen A or B should be taken seriously. Such a planet, if it exists, would perturb the orbital astrometry by <10μas, which is 10−6 of the separation between the two stars. We assess the feasibility of detecting such perturbations using ground-based intensity interferometry. We simulate a dedicated setup consisting of four 40-cm telescopes equipped with photon counters and correlators with time resolution $0.1\, \rm ns$, and a sort of matched filter implemented through an aperture mask. The astrometric error from one night of observing α Cen AB is $\approx 0.5\, \rm mas$. The error decreases if longer observing times and multiple spectral channels are used, as (channels × nights)−1/2.