We use N-body simulations to explore the possibility that the Sagittarius (Sgr) dwarf galaxy was originally a late-type, rotating disc galaxy, rather than a non-rotating, pressure-supported dwarf spheroidal galaxy, as previously thought. We find that bifurcations in the leading tail of the Sgr stream, similar to those detected by the SDSS survey, naturally arise in models where the Sgr disc is misaligned with respect to the orbital plane. Moreover, we show that the internal rotation of the progenitor may strongly alter the location of the leading tail projected on the sky, and thus affect the constraints on the shape of the Milky Way dark matter halo that may be derived from modelling the Sgr stream. Our models provide a clear, easily tested prediction; although tidal mass stripping removes a large fraction of the original angular momentum in the progenitor dwarf galaxy, the remnant core should still rotate with a velocity amplitude ~20kms-1 that could be readily detected in future, wide-field kinematic surveys of the Sgr dwarf.