We present evidence from a sample of 544 galaxies from the DEEP2 Survey for evolution of the internal kinematics of blue galaxies with stellar masses ranging 8.0 < { log } M _ { * } ( M _ { \odot } ) < 10.7 over 0.2 < z < 1.2 . DEEP2 provides galaxy spectra and Hubble imaging from which we measure emission-line kinematics and galaxy inclinations , respectively . Our large sample allows us to overcome scatter intrinsic to galaxy properties in order to examine trends in kinematics . We find that at a fixed stellar mass galaxies systematically decrease in disordered motions and increase in rotation velocity and potential well depth with time . Massive galaxies are the most well-ordered at all times examined , with higher rotation velocities and less disordered motions than less massive galaxies . We quantify disordered motions with an integrated gas velocity dispersion corrected for beam smearing ( \sigma _ { g } ) . It is unlike the typical pressure-supported velocity dispersion measured for early type galaxies and galaxy bulges . Because both seeing and the width of our spectral slits comprise a significant fraction of the galaxy sizes , \sigma _ { g } integrates over velocity gradients on large scales which can correspond to non-ordered gas kinematics . We compile measurements of galaxy kinematics from the literature over 1.2 < z < 3.8 and do not find any trends with redshift , likely for the most part because these datasets are biased toward the most highly star-forming systems . In summary , over the last \sim 8 billion years since z = 1.2 , blue galaxies evolve from disordered to ordered systems as they settle to become the rotation-dominated disk galaxies observed in the Universe today , with the most massive galaxies being the most evolved at any time .