The Giant Magellan Telescope (GMT) consists of seven 8.365 m segments, with gaps of 0.345 m between adjacent segments. A unique challenge for GMT lies in phasing the segments and, in particular, how to measure segment piston optically while the telescope is in science operation. In this paper, we present a dispersed fringe sensor (DFS) to make these measurements using a novel algorithm. We show that using four off-axis DFSs operating at J-band with 10 ms exposures, we are able to measure segment piston to the required 50 nm accuracy every 30 s with over 90% sky coverage.