We present ab initio theoretical results for the giant magnetoresistance of single-wall carbon nanotubes (CNT) in contact with nickel electrodes. These show that Ni atoms located on the surface or axis of CNT contacts can induce a significant magnetic moment on the carbon atoms. For non-gated, undoped CNTs, this produces room-temperature GMR ratios of between 45% and 100% of the anti-aligned conductance.