In this paper, we propose a novel free-space optical (FSO) communication system utilizing optical skyrmions. We introduce a scheme referred to as skyrmion number modulation (SkM), which employs index modulation by encoding information onto the skyrmion number, a topological invariant preserved during free-space propagation. This topological nature offers the potential for inherent robustness against atmospheric turbulence-induced wavefront distortions, which limit the performance of conventional FSO systems. More specifically, we demonstrate that the fluctuation of the received skyrmion number is mitigated by a proposed intensity-based masking technique. Finally, our performance analysis based on a discrete memoryless channel framework confirms that the proposed system exhibits near-ideal robustness under weak turbulence and supports high-order modulation in moderate regimes.