  We present a theoretical study of the radiative pion photoproduction on the
nucleon ($\gamma N \to \pi N \gamma'$) in the $\De$-resonance region, with the
aim to determine the magnetic dipole moment (MDM) of the $\Delta^+(1232)$. The
study is done within the framework of chiral effective-field theory where the
expansion is performed (to next-to-leading order) in the $\delta$
power-counting scheme which is an extension of chiral perturbation theory to
the $\Delta$-resonance energy region. We present the results for the absorptive
part of the $\Delta$ MDM, as well as perform a sensitivity study of the
dependence of $\gamma N \to \pi N \gamma'$ observables on the real part of the
$\Delta$ MDM. We find that an asymmetry for circular polarization of the photon
beam may provide a model-independent way to measure the $\Delta$ MDM.
