The collinear factorization framework allows to describe the exclusive photoproduction of a $\gamma \rho$ pair in the generalized Bjorken regime in terms of a perturbatively calculable coefficient function and universal generalized parton distributions. The kinematics are defined by a large invariant mass of the $\gamma \rho$ pair and a small transverse momentum of the final nucleon. We calculate the scattering amplitude at leading order in $\alpha_s$ and the differential cross sections for the process where the
$\rho$−meson is either longitudinally or transversely polarized, in the kinematics of the near future Jlab experiments. Our estimate of the cross section demonstrates that this process is measurable at JLab 12-GeV.