Abstract Effects of a dc current annealing, in terms of magnitude and inflow time, on magnetic hysteresis properties, magnetoimpedance (MI) and stress-magnetoimpedance (S-MI) in glass-coated amorphous Co71Fe5B11Si10Cr3 microwires with a small positive magnetostriction were investigated in this work. The annealing process combining Joule-heating and circular magnetic field leads to the creation of a specific magnetic anisotropy of a helical or circular type, and consequently, is helpful to control the MI and S-MI behaviours making them more suitable for particular sensing applications. After annealing, the magnetoimpedance plots transformed from a bell-shaped typical of an axial easy anisotropy to the shape with two symmetrical peaks, the magnitude and position of which are controlled with the annealing current parameters. Applying a tensile stress on the annealed wires changes the easy anisotropy direction which leads to the potential for highly sensitive S-MI without use of dc bias fields. A stress sensitivity of more than 260% at σ ex = 250 MPa at zero magnetic field is achieved.