High-resolution X-ray imaging offers a unique opportunity to probe the nature of dust in the z less than or similar to 2 universe. Dust grains 0.1-1 mu m in size will scatter soft X-rays, producing a diffuse "halo" image around an X-ray point source, with a brightness of similar to few percent confined to an arcminute-sized region. We derive the formulae for scattering in a cosmological context and calculate the surface brightness of the scattering halo due to (1) an intergalactic medium (IGM) uniformly enriched (Omega(d) similar to 10(-5)) by a power-law distribution of grain sizes and (2) a damped Ly alpha type (N-H similar to 10(21) cm(-2)) dust screen at cosmological distances. The morphology of the surface brightness profile can distinguish between the two scenarios above, place size constraints on dusty clumps, and constrain the homogeneity of the IGM. Thus, X-ray scattering can gauge the relative contribution of the first stars, dwarf galaxies, and galactic outflows to the cosmicmetallicity budget and cosmic history of dust. We show that, because the amount of intergalactic scattering is overestimated for photon energies < 1 keV, the non-detection of an X-ray scattering halo by Petric et al. is consistent with "gray" intergalactic dust grains (Omega(d) similar to 10(-5)) when the data are restricted to the 1-8 keV band. We also calculate the systematic offset in magnitude, delta m similar to 0.01, for such a population of graphite grains, which would affect the type of supernova survey ideal for measuring dark energy parameters within similar to 1% precision.