The spectral function for an electron one-component plasma is calculated self-consistently using the GW;{(0)} approximation for the single-particle self-energy. In this way, correlation effects that go beyond the mean-field description of the plasma are contained, i.e., the collisional damping of single-particle states, the dynamical screening of the interaction, and the appearance of collective plasma modes. Second, a nonperturbative analytic solution for the on-shell GW;{(0)} self-energy as a function of momentum is presented. It reproduces the numerical data for the spectral function with a relative error of less than 10% in the regime where the Debye screening parameter is smaller than the inverse Bohr radius, kappa<1a_{B};{-1} . In the limit of low density, the nonperturbative self-energy behaves as n;{14} , whereas a perturbation expansion leads to the unphysical result of a density-independent self-energy [Fennel and Wilfer, Ann. Phys. (Leipzig) 32, 265 (1974)]. The derived expression will greatly facilitate the calculation of observables in correlated plasmas (transport properties, equation of state) that need the spectral function as an input quantity. This is demonstrated for the shift of the chemical potential, which is computed from the analytical formulas and compared to the GW;{(0)} result. At a plasma temperature of 100eV and densities below 10;{21}cm;{-3} , the two approaches deviate by less than 10% from each other.