  We present kinematic orientations and high resolution (150 pc) rotation
curves for 67 main sequence star-forming galaxies surveyed in CO (2-1) emission
by PHANGS-ALMA. Our measurements are based on the application of a new fitting
method tailored to CO velocity fields. Our approach identifies an optimal
global orientation as a way to reduce the impact of non-axisymmetric (bar and
spiral) features and the uneven spatial sampling characteristic of CO emission
in the inner regions of nearby galaxies. The method performs especially well
when applied to the large number of independent lines-of-sight contained in the
PHANGS CO velocity fields mapped at 1'' resolution. The high resolution
rotation curves fitted to these data are sensitive probes of mass distribution
in the inner regions of these galaxies. We use the inner slope as well as the
amplitude of our fitted rotation curves to demonstrate that CO is a reliable
global dynamical mass tracer. From the consistency between photometric
orientations from the literature and kinematic orientations determined with our
method, we infer that the shapes of stellar disks in the mass range of log($\rm
M_{\star}(M_{\odot})$)=9.0-10.9 probed by our sample are very close to circular
and have uniform thickness.
