  We consider the effects of radio-wave scattering by cool ionized clumps
($T\sim 10^4\,$K) in circumgalactic media (CGM). The existence of such clumps
are inferred from intervening quasar absorption systems, but have long been
something of a theoretical mystery. We consider the implications for compact
radio sources of the `fog-like' two-phase model of the circumgalactic medium
recently proposed by McCourt et al.(2018). In this model, the CGM consists of a
diffuse coronal gas ($T\gtrsim 10^6\,$K) in pressure equilibrium with numerous
$\lesssim 1\,$pc scale cool clumps or `cloudlets' formed by shattering in a
cooling instability. The areal filling factor of the cloudlets is expected to
exceed unity in $\gtrsim 10^{11.5} M_\odot$ haloes, and the ensuing radio-wave
scattering is akin to that caused by turbulence in the Galactic warm ionized
medium (WIM). If $30\,$per-cent of cosmic baryons are in the CGM, we show that
for a cool-gas volume fraction of $f_{\rm v}\sim 10^{-3}$, sources at $z_{\rm
s}\sim 1$ suffer angular broadening by $\sim 15\,\mu$as and temporal broadening
by $\sim 1\,$ms at $\lambda = 30\,$cm, due to scattering by the clumps in
intervening CGM. The former prediction will be difficult to test (the angular
broadening will suppress Galactic scintillation only for $<10\,\mu$Jy compact
synchrotron sources). However the latter prediction, of temporal broadening of
localized fast radio bursts, can constrain the size and mass fraction of cool
ionized gas clumps as function of halo mass and redshift, and thus provides a
test of the model proposed by McCourt et al.(2018).
