The reaction gammap-->pi(0)gamma'p has been measured with the TAPS calorimeter at the Mainz Microtron accelerator facility MAMI for energies between sqrt[s]=1221-1331 MeV. The cross section's differential in angle and energy have been determined for the photon gamma' 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(+1.0)(-1.3)(stat)+/-1.5(syst)+/-3(theor)]mu(N) has been extracted.