We present a continuum model for spontaneous twisting of graphene nanoribbons driven by compressive edge stresses. Based on a geometrically nonlinear theory of plates, we identify scaling laws for the dependence of twist angles on ribbon width. Strikingly, we find the existence of a critical width below which a ribbon will not undergo spontaneous twisting, preferring an in-plane stretching mode instead. The model predictions are shown to be in excellent qualitative and quantitative agreement with density-functional tight-binding simulations. More generally, our model provides a unifying picture of twisting in graphene nanoribbons with different edge orientations and chemical functionalizations that have been reported recently in the literature.