Spin-dependent WIMPs in DAMA?

We investigate whether the annual modulation observed in the DAMA experimen t can be due to a weakly-interacting massive particle (WIMP) with an axial- vector (spin-dependent; SD) coupling to nuclei. We evaluate the SD WIMP-pro ton cross section under the assumption that such scattering accounts for th e DAMA modulation, and we do the same for a SD WIMP-neutron cross section. We show that SD WIMP-proton scattering is ruled out in a model-independent fashion by null searches for energetic neutrinos from WIMP annihilation in the Sun, and that SD WIMP-neutron scattering is ruled out for WIMP masses g reater than or similar to 20 GeV by the null result with the DAMA Xe detect or. A SD WIMP with mass less than or similar to 20 GeV is still compatible, but only if the SD WIMP-neutron interaction is four orders of magnitude gr eater than the WIMP-proton interaction.