Near-field coseismic perturbations of ionospheric total electron content (TEC), caused by direct acoustic waves from focal regions, can be observed with Global Positioning System (GPS). They appear 10--15 min after the earthquake with typical periods of ~4--5 min and propagate as fast as ~1 km/s toward directions allowed by ambient geomagnetic fields. Ionospheric disturbance, associated with the 2004 December 26 great Sumatra-Andaman earthquake, was recorded with nine continuous GPS receiving stations in Indonesia and Thailand. Here we explore the possibility to constrain the rupture process of the earthquake with the observed ionospheric disturbances. We assumed linearly distributed point sources along the zone of coseismic uplift extending ~1300 km from Sumatra to the Andaman Islands that excited acoustic waves sequentially as the rupture propagate northward by 2.5 km/s. TEC variations for several satellite-receiver pairs were synthesized by simulating the propagation of acoustic waves from the ground to the ionosphere and by integrating the TEC perturbations at intersections of line of sights and the ray paths. The TEC perturbations from individual point sources were combined using realistic ratios, and the total disturbances were compared with the observed signals. Prescribed ratios based on geodetically inferred coseismic uplifts reproduced the observed signals fairly well. Similar calculation using a rupture propagation speed of 1.7 km/s degraded the fit. Suppression of acoustic waves from the segments north of the Nicobar Islands also resulted in a poor fit, which suggests that ruptures in the northern half of the fault were slow enough to be overlooked in short-period seismograms but fast enough to excite atmospheric acoustic waves. Coseismic ionospheric disturbance could serve as a new indicator of faulting sensitive to ruptures with timescale up to 4--5 min.