In a substitutional alloy, the random nature of the electronic potential results in static spatial fluctuations of the electronic charge density. Previous work on the electronic structure of random substitutional alloys has been concerned only with the calculation of the configuration-averaged charge density of each alloy constituent. In the present work, three different perturbative techniques are used to calculate the mean-square fluctuation, <(Δn)2>, of the electronic occupation numbers about their average value for an independent electron model of a random substitutional alloy. In addition to determining the magnitude of charge fluctuations in random alloys, the results illustrate the dependence of charge fluctuations on the concentration and scattering strength of the alloy, the Fermi level, the crystal structure, and the orbital degeneracy. Simple estimates are made of the effect of Coulomb interactions on the charge fluctuations. Ordinarily these interactions suppress charge fluctuations, but, surprisingly, there are situations in which Coulomb interactions enhance the fluctuations. Rough numerical estimates of Δn indicate that, for alloys of the 5d transition metals Ta, W, Re, and Os, these charge fluctuations should be observable as a small increase (~0.5 eV) in the 4f core-level linewidth in x-ray photoemission measurements.