We report the first measurement of target single spin asymmetries of charged kaons produced in semi-inclusive deep inelastic scattering of electrons off a transversely polarized He-3 target. Both the Collins and Sivers moments, which are related to the nucleon transversity and Sivers distributions, respectively, are extracted over the kinematic range of 0.1 < x(bj) < 0.4 for K+ and K- production. While the Collins and Sivers moments for K+ are consistent with zero within the experimental uncertainties, both moments for K- favor negative values. The Sivers moments are compared to the theoretical prediction from a phenomenological fit to the world data. While the K+ Sivers moments are consistent with the prediction, the K- results differ from the prediction at the 2-sigma level.