The shift of a magnetization loop along the magnetic field axis for a ferromagnetic (FM)/anti-ferromagnetic (AFM) system when it is cooled through Néel temperature of AFM layer is called exchange anisotropy or exchange bias. Here, using micromagnetic simulations we propose that spin transfer torque (STT) mechanism would indeed be helpful in realizing the shift of the magnetization loop along magnetic field axis through domain wall (DW) resistance for an infinitely long FM nanowire without having AFM layer, which we call as spin transfer torque bias (STTB). Essentially, STTB is realized on both positive and negative magnetic field axes by varying the angle between spin polarized current and Zeeman field from 0 to 180 respectively and the origin is attributed to helical motion of the DW. However, we do not see STTB at 90 due to coherent rotation of domain. We also ascertain that STTB is also a function of magnetic anisotropy, current density, polarization strength and non-adiabatic STT term. Variation in STTB for different FM systems such as Fe2CoSi, Ni80Fe20 and Fe is attributed to a change in DW width. We believe that present results would lead to a new dimension in the field of spintronics. © 2021 IOP Publishing Ltd.