  We study the decay $B_c \rightarrow D_s^* \gamma$. There are two mechanisms
contributing to the process. One proceeds through the short distance
$b{\rightarrow}s\gamma$ transition and the other occurs through weak
annihilation accompanied by a photon emission.The electromagnetic penguin
contribution is estimated by perturbative QCD and found to be
$4.68\times10^{-18}$ GeV. In particular, we find the contribution of the weak
annihilation is $6.25\times10^{-18}GeV$ which is in the same order as that of
the electromagnetic penguin. The total decay rate $\Gamma(B_c \rightarrow D_s^*
\gamma)$ is predicted to be $1.45\times10^{-17}GeV$ and the branching ratio
$Br(B_c \rightarrow D_s^* \gamma)$ is predicted to be $2.98\times 10^{-5}$ for
$\tau_{B_c}=1.35ps$. The the decays $B_c \rightarrow D_s^* \gamma$ can be well
studied at LHC in the near future.
