We present observations of 12C32S, 12C34S, 13C32S, and 12C33S J=2-1 lines toward a large sample of massive star-forming regions by using the Arizona Radio Observatory 12m telescope and the IRAM 30m. Taking new measurements of the carbon 12C/13C ratio, the 32S/34S isotope ratio was determined from the integrated 13C32S/12C34S line intensity ratios for our sample. Our analysis shows a 32S/34S gradient from the inner Galaxy out to a galactocentric distance of 12kpc. An unweighted least-squares fit to our data yields 32S/34S=(1.56{+/-}0.17)DGC+(6.75{+/-}1.22) with a correlation coefficient of 0.77. Errors represent 1{sigma} standard deviations. Testing this result by (a) excluding the Galactic center region, (b) excluding all sources with C34S opacities >0.25, (c) combining our data and old data from previous study, and (d) using different sets of carbon isotope ratios leads to the conclusion that the observed 32S/34S gradient is not an artifact but persists irrespective of the choice of sample and carbon isotope data. A gradient with rising 32S/34S values as a function of galactocentric radius implies that the solar system ratio should be larger than that of the local interstellar medium. With the new carbon isotope ratios, we indeed obtain a local 32S/34S isotope ratio about 10% below the solar system one, as expected in the case of decreasing 32S/34S ratios with time and increased amounts of stellar processing. However, taking older carbon isotope ratios based on a lesser amount of data, such a decrease is not seen. No systematic variation of 34S/33S ratios along galactocentric distance was found. The average value is 5.9{+/-}1.5, the error denoting the standard deviation of an individual measurement.