We present a study of the orbit of the pre-main-sequence binary system GG Tau A and its relation to its circumbinary disk, in order to find an explanation for the sharp inner edge of the disk. Three new relative astrometric positions of the binary were obtained with NACO at the VLT. We combine these with data from the literature and fit orbit models to the dataset. We find that an orbit coplanar with the disk and compatible with the astrometric data is too small to explain the inner gap of the disk. On the other hand, orbits large enough to cause the gap are tilted with respect to the disk. If the disk gap is indeed caused by the stellar companion, then the most likely explanation is a combination of underestimated astrometric errors and a misalignment between the planes of the disk and the orbit.