  We derive holographic AdS/QCD Distribution Amplitudes for the transversely
polarised $\rho$ meson and we use them to predict the branching ratio for the
decays $\bar B^\circ\rightarrow \rho^\circ \gamma$ and $\bar
B^\circ_s\rightarrow \rho^\circ \gamma$ beyond leading power accuracy in the
heavy quark limit. For $\bar B^\circ\rightarrow \rho^\circ \gamma$, our
predictions agree with those generated using Sum Rules (SR) Distribution
Amplitudes and with the data from the BaBar and Belle collaborations. In
computing the weak annihilation amplitude which is power-supressed in $\bar
B^\circ\rightarrow \rho^\circ \gamma$ but is the leading contribution in
$\bar{B}^{\circ}_s\rightarrow \rho^\circ \gamma$, we find that, in its present
form, the AdS/QCD DA avoids the end-point divergences encountered with the SR
DA .
