  We use QCD sum rules to calculate the width of the radiative decay of the
meson X(3872), assumed to be a mixture between charmonium and exotic molecular
$[c\bar{q}][q\bar{c}]$ states with $J^{PC}=1^{++}$. We find that in a small
range for the values of the mixing angle, $5^0\leq\theta\leq13^0$, we get the
branching ratio $\Gamma(X\to J/\psi\gamma)/\Gamma(X\to
J/\psi\pi^+\pi^-)=0.19\pm0.13$, which is in agreement, with the experimental
value. This result is compatible with the analysis of the mass and decay width
of the mode $J/\psi(n\pi)$ performed in the same approach.
