The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long-range correlations, which behave as $\ensuremath{\sim}1/r$ in three and $\ensuremath{\sim}\mathrm{ln}(L/r)$ in two dimensions. We calculate the corresponding structure factors over the whole range of wave numbers, and find good agreement with two-dimensional molecular dynamics simulations. It is also shown by means of a mode coupling calculation, how the mean field values for the steady-state temperature and collision frequency, as obtained from the Enskog-Boltzmann equation, are renormalized by long wavelength hydrodynamic fluctuations.