We report the successful performance of the Robotic Optical Transient Search Experiment (ROTSE) to promptly-disseminated Swift GRB triggers. ROTSE-III is a worldwide network of 4 unfiltered 0.45m optical telescopes. The telescopes operate robotically, automatically responding to GRB position triggers with a preset observations sequence. Including weather and other downtime, ROTSE-III can immediately respond to similar to 40% of Swift trigger positions, with shutter open within approximately 6-8 seconds from the trigger dissemination. We discuss improvements made possible in the automated response the the small, accurate Swift error boxes. We report ROTSE-III's general results, including OTs discovered or confirmed, the distribution of imaging start times relative to the GRB duration, and an overview of OT lightcurves.