Variability in the sulfur isotopic composition in sediments can reflect atmospheric, geologic and biological processes. Evidence for ancient fluvio-lacustrine environments at Gale crater on Mars and a lack of efficient crustal recycling mechanisms on the planet suggests a surface environment that was once warm enough to allow the presence of liquid water, at least for discrete periods of time, and implies a greenhouse effect that may have been influenced by sulfur-bearing volcanic gases. Here we report in situ analyses of the sulfur isotopic compositions of SO2 volatilized from ten sediment samples acquired by NASA's Curiosity rover along a 13 km traverse of Gale crater. We find large variations in sulfur isotopic composition that exceed those measured for Martian meteorites and show both depletion and enrichment in 34S. Measured values of Δ34S range from - 47 ± 14‰ to 28 ± 7‰, similar to the range typical of terrestrial environments. Although limited geochronological constraints on the stratigraphy traversed by Curiosity are available, we propose that the observed sulfur isotopic signatures at Gale crater can be explained by equilibrium fractionation between sulfate and sulfide in an impact-driven hydrothermal system and atmospheric processing of sulfur-bearing gases during transient warm periods.