We study the magnetic susceptibility of a layered semiconductor BiTeI with giant Rashba spin splitting both theoretically and experimentally to explore its orbital magnetism. Apart from the core contributions, a large temperature-dependent diamagnetic susceptibility is observed when the Fermi energy E(F) is near the crossing point of the Rashba spin-split conduction bands at the time-reversal symmetry point A. On the other hand, when E(F) is below this band crossing, the susceptibility turns to be paramagnetic. These features are consistent with first-principles calculations, which also predict an enhanced orbital magnetic susceptibility with both positive and negative signs as a function of E(F) due to band (anti)crossings. Based on these observations, we propose two mechanisms for the enhanced paramagnetic orbital susceptibility.