Plastic deformation in body centered cubic iron is dominated by glide of screw dislocations with non-planar dislocation cores. This causes a strong strain rate and temperature dependence of flow stress, the breakdown of Schmid’s law and a dependence of dislocation mobility on shear stress components that do not contribute to the mechanical driving force for dislocation glide. Based on the framework of crystal plasticity, we developed a constitutive plasticity model that takes all these phenomena into account. To parameterize this continuum plasticity model molecular statics simulations using a semi-empirical potential have been performed. These atomistic calculations yielded quantitative relationships for the influence of all components of the local stress tensor on dislocation mobility. Together with experimental data from the literature on the kinetics of screw dislocations in bcc iron the constitutive relation presented here has been developed. As application example of the model, we calculated the tension compression asymmetry and the strain rate dependence of the hardening behavior within a bcc iron crystal.