We present a robust and exact method for calculating the polarization function and plasmon dispersion of graphene, for an arbitrary (isotropic) non-equilibrium carrier distribution, within random phase approximation (RPA). This is demonstrated for a range of carrier distributions, including
hot carrier distributions which occur within the femtoseconds following photoexcitation. We show that qualitatively different behaviour from the equilibrium case can occur. As the polarization function determines dynamic screening, its calculation shall be essential to quantifying carrier-carrier scattering channels for graphene far from equilibrium.