The application of the optical vortex interferometer (OVI) to small-angle rotation measurements is presented. The OVI is based on a regular lattice of optical vortices. In our experimental setup a regular lattice of optical vortices is produced by the interference of three plane waves. The vortex points are stable, pointlike structures within the interference field. Distortion of one, two, or three of the interference waves results in a characteristic vortex lattice deformation. This deformation can be measured and related to the physical quantities being investigated. We show the ability of the OVI to measure the deflection angle and the orientation of the wave vector in a single measurement. Two different methods that allow comparing the geometry of the vortex lattice are used to analyze the results of the experiment. They are compared with the method based on standard two-beam interferograms. The results show that the OVI system can be successfully used to measure the deflection and orientation of the wave vector. The vortex methodology is more accurate than classical two-beam interferometry for rotation angles in the range of a few arcseconds.