  The radial acceleration relation (RAR) in galaxies describes a tight
empirical scaling law between the total acceleration
$g_\mathrm{tot}(r)=GM_\mathrm{tot}(<r)/r^2$ observed in galaxies and that
expected from their baryonic mass $g_\mathrm{bar}(r)=GM_\mathrm{bar}(<r)/r^2$,
with a characteristic acceleration scale of $g_\dagger\simeq 1.2\times
10^{-10}$ms$^{-2}$. Here, we examine if such a correlation exists in galaxy
clusters using weak-lensing, strong-lensing, and X-ray data sets available for
20 high-mass clusters targeted by the CLASH survey. By combining our CLASH data
with stellar mass estimates for the brightest cluster galaxies (BCGs) and
accounting for the stellar baryonic component in clusters, we determine, for
the first time, an RAR on BCG--cluster scales. The resulting RAR is well
described by a tight power-law relation, $g_\mathrm{tot}\propto
g_\mathrm{bar}^{0.51^{+0.04}_{-0.05}}$, with lognormal intrinsic scatter of
$14.7^{+2.9}_{-2.8}\%$. The slope is consistent with the low acceleration limit
of the RAR in galaxies, $g_\mathrm{tot}=\sqrt{g_\dagger\,g_\mathrm{bar}}$,
whereas the intercept implies a much higher acceleration scale of $g_\ddagger =
(2.02\pm0.11)\times 10^{-9}$ms$^{-2}$, indicating that there is no universal
RAR that holds on all scales from galaxies to clusters. We find that the
observed RAR in CLASH clusters is consistent with predictions from a
semi-analytical model developed in the standard $\Lambda$CDM framework. Our
results also predict the presence of a baryonic Faber--Jackson relation
($\sigma_v^4\propto M_\mathrm{bar}$) on cluster scales.
