Mercury's low surface reflectance and the low surface abundances of iron and titanium have led to the suggestion that carbon (C) may serve as the dominant darkening agent on Mercury's surface. Estimates of the amount of carbon required to achieve the observed surface darkening are within the sensitivity range of measurements by MESSENGER's Gamma-Ray Spectrometer (GRS). We use GRS measurements to constrain the C content of Mercury's surface, the first such use of gamma-ray spectroscopy data. Our methodology includes techniques for removing background contributions to the measured signal and is broadly applicable to any gamma-ray spectroscopy dataset. The measured C content for Mercury's surface, 1.4±0.9 wt%, is consistent with 0 to 4.1 wt% C at the three-standard-deviation level and therefore does not represent a definitive detection of C at the surface. Possible mechanisms for providing up to 4.1 wt% C on Mercury's surface include primordial and exogenous sources. Additional measurements at low altitude made with MESSENGER's Neutron Spectrometer can yield further constraints on the C content of Mercury's surface.