We study the Delta^{++} contributions to elastic and radiative \pi^+pscattering within an effective Lagrangian model which incorporates the Delta,N, rho and sigma meson degrees of freedom. This model provides a description ofthe Delta resonance and its interactions that respects electromagnetic gaugeinvariance and invariance under contact transformations when finite widtheffects are incorporated. Following recent developments in the description ofunstable gauge bosons, we use a complex mass scheme to introduce the finitewidth of the Delta^{++} without spoiling gauge invariance. The total crosssection of elastic \pi^+p scattering, whose amplitude exhibits the resonantplus background structure of S-matrix theory, is used to fix the mass, widthand strong coupling of the \Delta resonance. The differential cross section ofelastic scattering is found in very good agreement with experimental data. Themagnetic dipole moment of the Delta^{++}, \mu_{Delta}, is left as the onlyadjustable parameter in radiative \pi^+p scattering. From a fit to the mostsensitive configurations for photon emission in this process, we obtain\mu_{\Delta} = (6.14 +-0.51)e/2m_p, in agreement with predictions based on theSU(6) quark model.