The shear-thinning fluid flow in rough fractures is of wide interest in subsurface engineering. Inertial effects due to flow regime, fracture aperture variations as well as fluid rheology affect the macroscopic flow parameters in an interrelated way. We present a 3D microscale flow simulation for both Newtonian and Cross power-law shear-thinning fluids through a rough fracture over a range of flow regimes, thus evaluating the critical Reynolds number above which the linear Darcy's law is no longer applicable. The flow domain is extracted from a computed microtomography image of a fractured Berea sandstone. The fracture aperture is much more variable than any of the previous numerical or experimental work involving shear-thinning fluids, and simulations are 3D for the first time. We quantify the simulated velocity fields and propose a new correlation for shift factor (parameter relating in situ porous medium viscosity with bulk viscosity). The correlation incorporates tortuosity (parameter calculated either based only on fracture image or on detailed velocity field, if available) as well as a fluid-dependent parameter obtained from the analytical/semi-analytical solutions of the same shear-thinning fluids flow in a smooth slit. Our results show that the shift factor is dependent on both the fracture aperture distribution (not only the hydraulic/equivalent aperture) and fluid rheology properties. However, both the inertial coefficient and critical Reynolds number are functions of the fracture geometry only, which is consistent with a recent experimental study.