A measurement of the dipole anisotropy in the arrival directions of galactic cosmic positrons, electrons and protons has been performed with the Alpha Magnetic Spectrometer (AMS) onboard the International Space Station (ISS) using the first 6 years of data. Thanks to its wide field of view and to the inclination of the ISS orbit, AMS provides nearly full sky coverage in galactic coordinates, which allows to determine the three independent dipole components for each cosmic ray species. The results are consistent with isotropy for all three particle species and upper limits on the dipole amplitude have been derived. A 95% C.I. upper limit of $\delta<0.020$ and $\delta<0.005$ has been obtained for positrons and electrons, respectively, in the energy range 16 to 350 GeV, and $\delta<0.008$ for protons for rigidities above 300 GV.