Rosebud is located at 43°13'57" North, 100°51'11" West (43.232500, -100.853056).
According to the United States Census Bureau, the township has a total area of 13.12 mi2 (33.98 km2). 13.08 mi2 (33.87 km2) of it is land and 0.04 mi2 (0.11 km2) of it is covered by water. The total area is 0.31% water.
Rosebud is located in the Central Standard Time (CST) timezone, GMT-06:00. It observes Daylight Saving Time (DST).