The circumgalactic medium (CGM) contains information on gas flows around galaxies, such as accretion and supernova-driven winds, which are difficult to constrain from observations alone. Here, we use the high-resolution TNG50 cosmological magneto-hydrodynamical simulation to study the properties and kinematics of the CGM around star-forming galaxies in $10^{11.5}-10^{12}\;M_{\odot}$ halos at $z\simeq1$ using mock MgII absorption lines, which we generate by post-processing halos to account for photoionization in the presence of a UV background. We find that the MgII gas is a very good tracer of the cold CGM, which is accreting inwards at an inflow velocity of $\sim$50 km s$^{-1}$. For sightlines aligned with the galaxy's major axis, we find that MgII absorption lines are kinematically shifted due to the cold CGM's significant corotation at speeds up to 50% of the virial velocity for impact parameters up to 60 kpc. We compare mock MgII spectra to observations from the MusE GAs FLow and Wind (MEGAFLOW) survey of strong MgII absorbers ($EW^{2796\r{A}}_{0}>0.5 \; \r{A}$). After matching the equivalent width (EW) selection, we find that the mock MgII spectra reflect the diversity of observed kinematics and EWs from MEGAFLOW, even though the sightlines probe a very small fraction of the CGM. MgII absorption in higher-mass halos is stronger and broader than in lower-mass halos but has qualitatively similar kinematics. The median specific angular momentum of the MgII CGM gas in TNG50 is very similar to that of the entire CGM and only differs from non-CGM components of the halo by normalization factors of $\lesssim$ 1 dex.