  The reaction $\gamma p \to \pi^\circ \gamma^\prime p$ has been measured with
the TAPS calorimeter at the Mainz Microtron accelerator facility MAMI for
energies between $\sqrt{s}$ = 1221--1331 MeV. Cross sections differential in
angle and energy have been determined for all particles in the final state in
three bins of the excitation energy. This reaction channel provides access to
the magnetic dipole moment of the $\Delta^{+}(1232)$ resonance and, for the
first time, a value of $\mu_{\Delta^+} = (2.7_{-1.3}^{+1.0}(stat.) \pm 1.5
(syst.) \pm 3(theo.)) \mu_N$ has been extracted.
