  Over 80% of the cosmic baryon density is likely to be distributed in the
diffuse, $\gtrsim10^{4}$ K circum- and inter-galactic medium (CGM and IGM
respectively). We demonstrate that the dispersion measures (DMs) of samples of
localized Fast Radio Bursts (FRBs) can be used to measure the distribution of
baryons between the CGM and IGM. We propose to separate the CGM and IGM
contributions to FRB DMs by including redshift and mass measurements of
intervening galaxies. Using simulated samples of FRB sightlines through
intervening galaxy halos and an illustrative model for the CGM, and including
realistic observational uncertainties, we show that small samples
($O(10^{1})-O(10^{2})$) of localized FRBs are sensitive to the presence of CGM
gas. The fractions of baryons in the CGM and IGM can be accurately estimated
with 100 FRBs at $z<1$, and the characteristic radial density profiles of CGM
halos may also be possible to constrain. The required samples of localized FRBs
are expected to be assembled in the coming few years by instruments such as the
Australian Square Kilometre Array Pathfinder, the Very Large Array, and the
Deep Synoptic Array.
