The Martian atmosphere and the CO2 polar ice caps exchange mass. This exchange, together with the atmospheric response to solar heating, induces variations of the rotation of Mars. Using the angular momentum budget equation of the system solid-Mars--atmosphere--polar ice caps, the variations of Mars' rotation can be deduced from the variations of the angular momentum of the superficial layer; this later is associated with the winds, that is, the motion term, and with the mass redistribution, that is, the matter term. For the mean Martian atmosphere, without global dust storms, total amplitudes of 10 cm on the surface are obtained for both the annual and semiannual polar motion excited by the atmosphere and ice caps. The atmospheric pressure variations are the dominant contribution to these amplitudes. Length-of-day (lod) variations have amplitudes of 0.253 ms for the annual signal and of 0.246 ms for the semiannual signal. The lod variations are mainly associated with changes in the atmospheric contribution to the mass term, partly compensated by the polar ice cap contribution. We computed lod variations and polar motion for three scenarios having different atmospheric dust contents. The differences between the three sets of results for lod variations are about one order of magnitude larger than the expected accuracy of the NEtlander Ionosphere and Geodesy Experiment (NEIGE) for lod. It will thus be possible to constrain the global atmospheric circulation models from the NEIGE measurements.