  We calculate the asymmetries for the processes $\vec\gamma+\vec p\to
\Lambda_c^+ (\Sigma_c^+)+\bar{D^0}$ and $\vec\gamma+\vec p\to \Lambda_c^+
(\Sigma_c^+)+\bar{D^*}$, induced by circularly polarized photons on a polarized
proton target in the framework of an effective Lagrangian model. We found large
and positive values for the asymmetry induced by the $z-$component of the
proton polarization, in a wide energy region, from threshold up to
$E_\gamma=70$ GeV. In the case of pseudoscalar meson photoproduction, the
predictions are qualitatively model-independent. For $D^*$-photoproduction,
there is a strong dependence of the asymmetries on $N\Lambda_c D(D^*)$-coupling
constants.
