We analyze the effects of a randomly inhomogeneous spatial variation of the electrostatic potential across the flat surface of a doped graphene sheet on the spectral shape of its plasmon resonance in the terahertz to the mid-infrared frequency range. This is achieved by solving the plasmonic eigenvalue problem based on a position-dependent Drude conductivity of graphene, coupled with a stochastic description of the underlying random potential landscape, which is parameterized by a variance and a correlation length. We computed a frequency– and wavenumber–dependent spectral density, which exhibits strong nonlocal effects due to both the variance and the correlation length. Those parameters were found to play comparable roles in the plasmon line broadening and that they can give rise to the blue– or red–shifting of the plasmon peak. We also found that a substantial asymmetry develops in the plasmon spectra with increasing the disorder parameters and increasing frequency, causing a sizeable uncertainty in the positions of the peak and the mean values of those spectra in relation to the plasmon dispersion of clean graphene. The inclusion of the correlation length and the analysis of the spectral asymmetry are novel aspects of our work that were largely ignored in previous studies of the disorder effects in graphene plasmonics.