Numerous ongoing experiments aim at detecting WIMP dark matter particles from the galactic halo directly through WIMP-nucleon interactions .
Once such a detection is established a confirmation of the galactic origin of the signal is needed .
This requires a direction-sensitive detector .
We show that such a detector can measure the velocity anisotropy \beta of the galactic halo .
Cosmological N-body simulations predict the dark matter anisotropy to be nonzero , \beta \sim 0.2 .
Baryonic matter has \beta = 0 and therefore a detection of a nonzero \beta would be strong proof of the fundamental difference between dark and baryonic matter .
We estimate the sensitivity for various detector configurations using Monte Carlo methods and we show that the strongest signal is found in the relatively few high recoil energy events .
Measuring \beta to the precision of \sim 0.03 will require detecting more than 10 ^ { 4 } WIMP events with nuclear recoil energies greater than 100 keV for a WIMP mass of 100 GeV and a ^ { 32 } S target .
This number corresponds to \sim 10 ^ { 6 } events at all energies .
We discuss variations with respect to input parameters and we show that our method is robust to the presence of backgrounds and discuss the possible improved sensitivity for an energy-sensitive detector .