During the last glacial period, large millennial-scale temperature oscillations--the 'Dansgaard/Oeschger' cycles--were the primary climate signal in Northern Hemisphere climate archives from the high latitudes to the tropics. But whether the influence of these abrupt climate changes extended to the tropical and subtropical Southern Hemisphere, where changes in insolation are thought to be the main direct forcing of climate, has remained unclear. Here we present a high-resolution oxygen isotope record of a U/Th-dated stalagmite from subtropical southern Brazil, covering the past 116,200 years. The oxygen isotope signature varies with shifts in the source region and amount of rainfall in the area, and hence records changes in atmospheric circulation and convective intensity over South America. We find that these variations in rainfall source and amount are primarily driven by summer solar radiation, which is controlled by the Earth's precessional cycle. The Dansgaard/Oeschger cycles can be detected in our record and therefore we confirm that they also affect the tropical hydrological cycle, but that in southern subtropical Brazil, millennial-scale climate changes are not as dominant as they are in the Northern Hemisphere.