  The radial acceleration relation (RAR) represents a tight empirical relation
between the inferred total and baryonic centripetal accelerations,
$g_{\rm{tot}}=GM_{\rm{tot}}(<r)/r^2$ and $g_{\rm{bar}}=GM_{\rm{bar}}(<r)/r^2$,
observed in galaxies and galaxy clusters. The tight correlation between these
two quantities can provide insight into the nature of dark matter. Here we use
BAHAMAS, a state-of-the-art suite of cosmological hydrodynamical simulations,
to characterize the RAR in cluster-scale halos for both cold and collisionless
dark matter (CDM) and self-interacting dark matter (SIDM) models. SIDM halos
generally have reduced central dark matter densities, which reduces the total
acceleration in the central region when compared with CDM. We compare the RARs
in galaxy clusters simulated with different dark matter models to the RAR
inferred from CLASH observations. Our comparison shows that the cluster-scale
RAR in the CDM model provides an excellent match to the CLASH RAR obtained by
Tian et al. including the high-acceleration regime probed by the brightest
cluster galaxies (BCGs). By contrast, models with a larger SIDM cross-section
yield increasingly poorer matches to the CLASH RAR. Excluding the BCG regions
results in a weaker but still competitive constraint on the SIDM cross-section.
Using the RAR data outside the central $r<100$kpc region, an SIDM model with
$\sigma/m=0.3$cm$^{2}$g$^{-1}$ is disfavored at the $3.8\sigma$ level with
respect to the CDM model. This study demonstrates the power of the
cluster-scale RAR for testing the collisionless nature of dark matter.
