  We present an analysis of the angular momentum content of the circumgalactic
medium (CGM) using TNG100, one of the flagship runs of the IllustrisTNG
project. We focus on Milky Way-mass halos ($\sim 10^{12} \; M_{\odot}$) at
$z=0$ but also analyze other masses and redshifts up to $z=5$. We find that the
CGM angular momentum properties are strongly correlated with the stellar
angular momentum of the corresponding galaxy: the CGM surrounding high-angular
momentum galaxies has a systematically higher angular momentum and is better
aligned to the rotational axis of the galaxy itself than the CGM surrounding
low-angular momentum galaxies. Both the hot and cold phases of the CGM show
this dichotomy, though it is stronger for colder gas. The CGM of high-angular
momentum galaxies is characterized by a large wedge of cold gas with rotational
velocities at least $\sim1/2$ of the halo's virial velocity, extending out to
$\sim 1/2$ of the virial radius, and by biconical polar regions dominated by
radial velocities suggestive of galactic fountains; both of these features are
absent from the CGM of low-angular momentum galaxies. These conclusions are
general to halo masses $\lesssim 10^{12} \; M_{\odot}$ and for $z \lesssim 2$,
but they do not apply for more massive halos or at the highest redshift
studied. By comparing simulations run with alterations to the fiducial feedback
model, we identify the better alignment of the CGM to high-angular momentum
galaxies as a feedback-independent effect and the galactic winds as a dominant
influence on the CGM's angular momentum.
