We study the polaronic effect on the differential cross section (DCS) for an electron Raman scattering process in a spherical anisotropic semiconductor quantum dot in the presence of a homogeneous external electric field. The Fröhlich coupling of electrons with confined and surface polar optical phonon modes for resonance Raman scattering is considered. The influence of electron-phonon coupling on the energy spectrum is taken into account in the framework of perturbation theory. The emission spectra are discussed for different anisotropy cases. Resonant peaks in the spectra are found and interpreted.