The magnetization reversal process in Co-rich glass-covered amorphous microwires has been studied in presence of the torsion stress. The experiments have been performed using the transverse magneto-optical Kerr effect in crossed axial and circular magnetic fields. The influence of the torsion stress on the surface domain structure has been investigated. The angle of the surface helical structure has been determined based on the analysis of the stress-induced transformation of the Kerr hysteresis loops. The dependence of the angle of the helical structure on the value of the torsion stress has been obtained.