We propose an observational test for gravitationally recoiling supermassive black holes (BHs) in active galactic nuclei, based on a correlation between the velocities of BHs relative to their host galaxies, |Δv|, and their obscuring dust column densities, Σ_dust (both measured along the line of sight). We use toy models for the distribution of recoil velocities, BH trajectories, and the geometry of obscuring dust tori in galactic centres, to simulate 2.5 × 10⁵ random observations of recoiling quasars. BHs with recoil velocities comparable to the escape velocity from the galactic centre remain bound to the nucleus, and do not fully settle back to the centre of the torus due to dynamical friction in a typical quasar lifetime. We find that |Δv| and Σ_dust for these BHs are positively correlated. For obscured (Σ_dust > 0) and for partially obscured (0 < Σ_dust ≲ 2.3 g m^-2) quasars with |Δv| ≥ 45 km s^-1, the sample correlation coefficient between log₁₀(|Δv|) and Σ_dust is r₄₅ = 0.28 ± 0.02 and r₄₅ = 0.13 ± 0.02, respectively. Allowing for random ± 100 km s^{– 1} errors in |Δv| unrelated to the recoil dilutes the correlation for the partially obscured quasars to r₄₅ = 0.026 ± 0.004 measured between |Δv| and Σ_dust. A random sample of ≳ 3500 obscured quasars with |Δv| ≥ 45 km s^-1would allow rejection of the no-correlation hypothesis with 3σ significance 95 per cent of the time. Finally, we find that the fraction of obscured quasars, {F_obs} (|Δv|), decreases with |Δv| from {F_obs} (<10 km s^-1) ≳ 0.8 to {F_obs} (>10³ km s^-1) ≲ 0.4. This predicted trend can be compared to the observed fraction of type II quasars, and can further test combinations of recoil, trajectory, and dust torus models.