Spatially resolved velocity profiles are presented for nine faint field galaxies in the redshift range 0.1 ≤ z ≤ 1, based on moderate-resolution spectroscopy obtained with the Keck 10 m telescope. These data were augmented with high-resolution Hubble Space Telescope images from WFPC2, which provided V and I photometry, galaxy type, orientation, and inclination. The effects of seeing, slit width, and slit misalignment with respect to galaxy major axis were modeled along with inclination for each source, in order to derive a maximum circular velocity from the observed rotation curve. The lowest redshift galaxy, though highly elongated, shows a distorted low-amplitude rotation curve that suggests a merger in progress seen perpendicular to the collision path. The remaining rotation curves appear similar to those of local galaxies in both form and amplitude, implying that some massive disks were in place at z ~ 1. The key result is that the kinematics of these distant galaxies show evidence for only a modest increase in luminosity (ΔMB ≤ 0.6) compared to velocity-luminosity (Tully-Fisher) relations for local galaxies.