  Within the framework of electroweak theory, we investigate the elastic
scattering process $ e^{-} + \nu_{\mu} \rightarrow e^{-} + \nu_{\mu}$ in the
presence of an intense elliptically polarized laser field. We derive an
analytical expression for the spin-unpolarized differential cross section using
the first Born approximation and the Dirac-Volkov states to describe the
incident and scattered electrons. Our results generalize those found for the
linearly polarized field by Bai \textit{et al.} [Phys. Rev. A \textbf{85},
013402 (2012)] and for the circularly polarized field by El Asri \textit{et
al.} [Phys. Rev. D \textbf{104}, 113001 (2021)]. We find that the differential
cross section is significantly enhanced for linear polarization and reduced for
circular and elliptical polarizations.
