Results of quantum mechanical simulations of the influence of edge disorder on transport in graphene nanoribbon metal oxide semiconductor field-effect transistors (MOSFETs) are reported. The addition of edge disorder significantly reduces ON-state currents and increases OFF-state currents, and introduces wide variability across devices. These effects decrease as ribbon widths increase and as edges become smoother. However the bandgap decreases with increasing width, thereby increasing the band-to-band tunneling mediated subthreshold leakage current even with perfect nanoribbons. These results suggest that without atomically precise edge control during fabrication, MOSFET performance gains through use of graphene will be difficult to achieve.