  We derive the frequency shifts and the broadening of $\Gamma$ point
longitudinal optical (LO) and transverse optical (TO) phonon modes, due to
electron-phonon interaction, in graphene under uniaxial strain as a function of
the electron density and the disorder amount. We show that, in the absence of a
shear strain component, such interaction gives rise to a lifting of the
degeneracy of the LO and TO modes which contributes to the splitting of the G
Raman band. The anisotropy of the electronic spectrum, induced by the strain,
results in a polarization dependence of the LO and TO modes. This dependence is
in agreement with the experimental results showing a periodic modulation of the
Raman intensity of the splitted G peak. Moreover, the anomalous behavior of the
frequency shift reported in undeformed graphene is found to be robust under
strain.
