We theoretically study the magnetoresistance of single wall carbon nanotubes (SWCNTs) in the ballistic transport regime, using a standard tight-binding approach. The main attention is directed to spin-polarized electrical transport in the presence of either axial or perpendicular magnetic field. The method takes into account both Zeeman splitting as well as size and chirality effects. These factors (along with a broadening of energy levels due to a strong nanotube/electrode coupling) lead, in ultra small SWCNTs, to serious modifications in profile of the Aharonov-Bohm oscillations. Other noteworthy findings are that in the parallel configuration (axial magnetic field) the ballistic magnetoconductance is negative (positive) for armchair (semiconducting zigzag) nanotubes, whereas in the perpendicular configuration the magnetoresistance is nearly zero both for armchair and zigzag SWCNTs.