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Using a three-dimensional, atomistic quantum transport simulator based on the tight-binding method, we investigate statistical samples of single-gate graphene nanoribbon (GNR) tunneling field-effect transistors (TFETs) with different line edge roughness probabilities. We find that as the nanoribbon edges become rougher, the device OFF-current drastically increases due to a reduction of the graphene band gap and an enhancement of source-to-drain tunneling leakage through the gate potential barrier. At the same time, the ON-current remains almost constant. This leads to a deterioration of the transistor subthreshold slopes and to unacceptably low ON/OFF current ratios limiting the switching performances of GNR TFETs.