The flow-theory version of couple stress plasticity is employed to investigate the asymptotic fields near a steadily propagating crack-tip, under Mode III loading conditions. By incorporating a material characteristic length, typically of the order of few microns for ductile metals, the adopted constitutive model accounts for the microstructure of the material and can capture the strong size effects arising at small scales. Due to the effects of microstructure, the singularities of the stress and couple stress fields increase substantially, also for small hardening. The skew-symmetric stress field is found to be more singular then couple stress fields, whereas the symmetric stress components are regular at the crack-tip. The performed asymptotic analysis can provide useful predictions about the increase of the traction level ahead of the crack-tip due to the strain gradient effects, which have been found relevant and non negligible at the micron scale.