Abstract: We test a particular theory of dark matter in which dark matter axions form ring "caustics" in the plane of the Milky Way against actual observations of Milky Way stars. According to this theory, cold, collisionless dark matter particles with angular momentum flow in and out of the Milky Way on sheets. These flows form caustic rings (at the positions of the rings, the density of the flow is formally infinite) at the locations of closest approach to the Galactic center. We show that the caustic ring dark matter theory reproduces a roughly logarithmic halo, with large perturbations near the rings. We show that the theory can reasonably match the observed rotation curve of the Milky Way. We explore the effects of the caustic rings on dwarf galaxy tidal disruption using N-body simulations. In particular, simulations of the Sagittarius dwarf galaxy tidal disruption in a caustic ring halo potential match observations of the trailing tidal tail as far as 90 kpc from the Galactic center; they do not, however, match the leading tidal tail. None of the caustic ring, NFW, or triaxial logarithmic halos fit all of the data. The source code for calculating the acceleration due to a caustic ring halo has been made publicly available in the NEMO Stellar Dynamics Toolbox and the Milkyway@home client repository.