Our knowledge of the circumgalactic medium (CGM) is mostly based on quasar absorption line measurements. These have uncovered a multiphase medium that is likely highly turbulent, but constraints of this turbulence are limited to measurements of the nonthermal width of absorption line components (b
turb) and the line-of-sight velocity dispersion between components (σ
LOS). Here we analyze a suite of CGM simulations to determine how well these indirect measures are related to the underlying CGM. Our simulations track the nonequilibrium evolution of all commonly observed ions and consist of two main types: small-scale simulations of regions of homogenous CGM turbulence and global simulations of inhomogenous turbulence throughout a galactic halo. From each simulation, we generate mock spectra of Si ii, Si iv, C iv, and O vi, which allow us to directly compare b
turb and σ
LOS to the true line-of-sight turbulence (σ
1D). In the small-scale simulations, b
turb is only weakly correlated with σ
1D, likely because it measures random motions within individual warm CGM clouds, which do not sample the overall random motions. Meanwhile, σ
LOS and σ
1D are strongly correlated with σ
1D ≈ σ
LOS + 10 km s−1 in the densest regions we simulated, although the strength of this correlation depended weakly on the gas phase being probed. Our large-scale simulations also indicate that b
turb and σ
1D are largely uncorrelated and that σ
1D ≈ σ
LOS + 10 km s−1 on average, although it varies along individual sight lines. Moreover, the σ
LOS distributions from our global simulations are similar to recent observations, suggesting that this quantity may provide useful constraints on circumgalactic turbulence regardless of the axis probed.