We use hydrodynamical simulations of two Milky Way-mass galaxies to demonstrate the impact of cosmic-ray pressure on the kinematics of cool and warm circumgalactic gas. Consistent with previous studies, we find that cosmic-ray pressure can dominate over thermal pressure in the inner 50 kpc of the circumgalactic medium (CGM), creating an overall cooler CGM than that of similar galaxy simulations run without cosmic rays. We generate synthetic sightlines of the simulated galaxies CGM and use Voigt profile fitting methods to extract ion column densities, Doppler-b parameters, and velocity centroids of individual absorbers. We directly compare these synthetic spectral line fits with HST/COS CGM absorption-line data analyses, which tend to show that metallic species with a wide range of ionization potential energies are often kinematically aligned. Compared to the Milky-Way simulation run without cosmic rays, the presence of cosmic-ray pressure in the inner CGM creates narrower OVI absorption features and broader SiIII absorption features, a quality which is more consistent with observational data. Additionally, because the cool gas is buoyant due to nonthermal cosmic-ray pressure support, the velocity centroids of both cool and warm gas tend to align in the simulated Milky Way with feedback from cosmic rays. Our study demonstrates that detailed, direct comparisons between simulations and observations, focused on gas kinematics, have the potential to reveal the dominant physical mechanisms that shape the CGM.