Intrinsic torque, which can be generated by turbulent stresses, can induce toroidal rotation in a tokamak plasma at rest without direct momentum injection. Reversals in intrinsic torque have been inferred from the observation of toroidal velocity changes in recent lower hybrid current drive (LHCD) experiments. This work focuses on understanding the cause of LHCD-induced intrinsic torque reversal using gyrokinetic simulations and theoretical analyses. A new mechanism for the intrinsic torque reversal linked to magnetic shear (͉) effects on the turbulence spectrum is identified. This reversal is a consequence of the ballooning structure at weak ͉. Based on realistic profiles from the Alcator C-Mod LHCD experiments, simulations demonstrate that the intrinsic torque reverses for weak ͉ discharges and that the value of ͉ crit is consistent with the experimental results ͉critexp ≈ 0.2 ∼ 0.3 [Rice et al., Phys. Rev. Lett. 111, 125003 (2013)]. The consideration of this intrinsic torque feature in our work is important for the understanding of rotation profile generation at weak ͉ and its consequent impact on macro-instability stabilization and micro-turbulence reduction, which is crucial for ITER. It is also relevant to internal transport barrier formation at negative or weakly positive ͉.