  Recent theoretical studies predict that the circumgalactic medium (CGM)
around low-redshift, $\sim L_*$ galaxies could have substantial nonthermal
pressure support in the form of cosmic rays. However, these predictions are
sensitive to the specific model of cosmic-ray transport employed, which is
theoretically and observationally underconstrained. In this work, we propose a
novel observational constraint for calculating the lower limit of the
radially-averaged, effective cosmic-ray transport rate, $\kappa_{\rm min}^{\rm
eff}$. Under a wide range of assumptions (so long as cosmic rays do not lose a
significant fraction of their energy in the galactic disk, regardless of
whether the cosmic-ray pressure is important or not in the CGM), we demonstrate
a well-defined relationship between $\kappa_{\rm min}^{\rm eff}$ and three
observable galaxy properties: the total hydrogen column density, the average
star formation rate, and the gas circular velocity. We use a suite of FIRE-2
galaxy simulations with a variety of cosmic-ray transport physics to
demonstrate that our analytic model of $\kappa_{\rm min}^{\rm eff}$ is a robust
lower limit of the true cosmic-ray transport rate. We then apply our new model
to calculate $\kappa_{\rm min}^{\rm eff}$ for galaxies in the COS-Halos sample,
and confirm this already reveals strong evidence for an effective transport
rate which rises rapidly away from the interstellar medium to values
$\kappa_{\rm min}^{\rm eff}\gtrsim 10^{30-31}\,{\rm cm}^2\,{\rm s}^{-1}$
(corresponding to anisotropic streaming velocities of $v^{\rm stream}_{\rm eff}
\gtrsim 1000\,{\rm km}\,{\rm s}^{-1}$) in the diffuse CGM, at impact parameters
larger than $50-100$\,kpc. We discuss how future observations can provide
qualitatively new constraints in our understanding of cosmic rays in the CGM
and intergalactic medium.
