  We explore the evolution of the internal gas kinematics of star-forming
galaxies from the peak of cosmic star-formation at $z\sim2$ to today.
Measurements of galaxy rotation velocity $V_{rot}$, which quantify ordered
motions, and gas velocity dispersion $\sigma_g$, which quantify disordered
motions, are adopted from the DEEP2 and SIGMA surveys. This sample covers a
continuous baseline in redshift from $z=2.5$ to $z=0.1$, spanning 10 Gyrs. At
low redshift, nearly all sufficiently massive star-forming galaxies are
rotationally supported ($V_{rot}>\sigma_g$). By $z=2$, the percentage of
galaxies with rotational support has declined to 50$\%$ at low stellar mass
($10^{9}-10^{10}\,M_{\odot}$) and 70$\%$ at high stellar mass
($10^{10}-10^{11}M_{\odot}$). For $V_{rot}\,>\,3\,\sigma_g$, the percentage
drops below 35$\%$ for all masses. From $z\,=\,2$ to now, galaxies exhibit
remarkably smooth kinematic evolution on average. All galaxies tend towards
rotational support with time, and it is reached earlier in higher mass systems.
This is mostly due to an average decline in $\sigma_g$ by a factor of 3 since a
redshift of 2, which is independent of mass. Over the same time period,
$V_{rot}$ increases by a factor of 1.5 for low mass systems, but does not
evolve for high mass systems. These trends in $V_{rot}$ and $\sigma_g$ with
time are at a fixed stellar mass and should not be interpreted as evolutionary
tracks for galaxy populations. When galaxy populations are linked in time with
abundance matching, not only does $\sigma_g$ decline with time as before, but
$V_{rot}$ strongly increases with time for all galaxy masses. This enhances the
evolution in $V_{rot}/\sigma_g$. These results indicate that $z\,=\,2$ is a
period of disk assembly, during which the strong rotational support present in
today's massive disk galaxies is only just beginning to emerge.
