  We investigate the radiative $B_{c} \to D_{s1} \gamma$ transition in the
framework of QCD sum rules. In particular, we calculate the transition form
factors responsible for this decay in both weak annihilation and
electromagnetic penguin channels using the quark condensate, mixed and
two-gluon condensate diagrams as well as propagation of the soft quark in the
electromagnetic field as non-perturbative corrections. These form factors are
then used to estimate the branching ratios of the channels under consideration.
The total branching ratio of the $B_{c} \to D_{s1} \gamma$ transition is
obtained to be in order of $10^{-5}$, and the dominant contribution comes from
the weak annihilation channel.
