The dipole anisotropy seen in the cosmic microwave background radiation is interpreted as due to our peculiar motion. The Cosmological Principle implies that this cosmic dipole signal should also be present, with the same direction, in the large-scale distribution of matter. Measurement of the cosmic matter dipole constitutes a key test of the standard cosmological model. Current measurements of this dipole are barely above the expected noise and unable to provide a robust test. Upcoming radio continuum surveys with the SKA should be able to detect the dipole at high signal to noise. We simulate number count maps for SKA survey specifications in Phases 1 and 2, including all relevant effects. Nonlinear effects from local large-scale structure contaminate the cosmic (kinematic) dipole signal, and we find that removal of radio sources at low redshift (z 0.5) leads to significantly improved constraints. We forecast that the SKA could determine the kinematic dipole direction in Galactic coordinates with an error of (∆l, ∆b) ∼ (9 • , 5 • ) to (8 • , 4 • ), depending on the sensitivity. The predicted errors on the relative speed are ∼ 10%. These measurements would significantly reduce the present uncertainty on the direction of the radio dipole, and thus enable the first critical test of consistency between the matter and CMB dipoles.where the direction is given in Galactic coordinates.This dipole is expected to be dominated by the kinematic contribution, which is O(10 2 ) larger than the intrinsic fluctuations in the standard ΛCDM model. Since the cosmic variance of the dipole is very large, significant non-kinematic contributions remain possible and need to be tested by other means. Probing the dipole of the matter distribution in addition to that of the CMB will help to tighten constraints on putative non-kinematic contributions.The extragalactic radio sky offers an excellent opportunity to perform an independent test of the Cosmological Principle. The radio continuum dipole is expected to be dominated by the kinematic dipole. This is not the case for galaxy surveys at visible or infrared wavebands: the number counts in wide area surveys in those wavebands are dominated by objects at redshifts well below unity, so that the large-scale structure dominates over the kinematic signal. By contrast, radio continuum surveys have median redshifts above one, which suppresses the effect of local large-scale structure. Another advantage is that radio waves are not subject to extinction and thus the sky area that can be reliably observed by radio surveys exceeds that of optical and infrared surveys.The largest available wide-area radio continuum surveys include the NRAO VLA Sky Survey (NVSS) (Condon et al. 1998) and the TIFR GMRT Sky Survey (TGSS) (Intema et al. 2016).