We study the impact on the galaxy correlation function of the presence of a vector component in the tracers' peculiar velocities, in the case in which statistical isotropy is violated. We present a general framework - based on the bipolar spherical harmonics expansion - to study this effect in a model independent way, without any hypothesis on the origin or the properties of these vector modes. We construct six new observables, that can be directly measured in galaxy catalogs in addition to the standard monopole, quadrupole and hexadecapole, and we show that they completely describe any deviations from isotropy. We then perform a Fisher analysis in order to quantify the constraining power of future galaxy surveys. As an example, we show that the SKA2 would be able to detect anisotropic rotational velocities with amplitudes as low as 1% of that of the vorticity generated during shell-crossing in standard dark matter scenarios.