A cryogenic fixed point cell has been filled with high purity (99.999%) sulfur hexafluoride (SF6) and measured in an adiabatic closed-cycle cryostat system. Temperature measurements of the SF6 melting curve were performed using a capsule-type standard platinum resistance thermometer (CSPRT) calibrated over the International Temperature Scale of 1990 (ITS-90) subrange from the triple point of equilibrium hydrogen to the triple point of water. The measured temperatures were corrected by 0.37 mK for the effects of thermometer self-heating, and the liquidus-point temperature estimated by extrapolation to melted fraction F = 1 of a simple linear regression versus melted fraction F in the range F = 0.53 to 0.84. Based on this measurement, the temperature of the triple point of sulfur hexafluoride is shown to be 223.555 23(49) K (k = 1) on the ITS-90. This value is in excellent agreement with the best prior measurements reported in the literature, but with considerably smaller uncertainty. An analysis of the detailed uncertainty budget of this measurement suggests that if the triple point of sulfur hexafluoride were to be included as a defining fixed point of the next revision of the International Temperature Scale, it could do so with a total realization uncertainty of approximately 0.43 mK, slightly larger than the realization uncertainties of the defining fixed points of the ITS-90. Since the combined standard uncertainty of this SF6 triple point temperature determination is dominated by chemical impurity effects, further research exploring gas purification techniques and the influence of specific impurity species on the SF6 triple point temperature may bring the realization uncertainty of SF6 as a fixed point material into the range of the defining fixed points of the ITS-90.