The effect of the dislocation density tensor is introduced into the classical crystal plasticity framework by means of the micromorphic theory of single crystals. A computational homogenisation strategy is presented in order to describe the global and local responses of two-dimensional polycrystalline aggregates for grain sizes ranging from 1 to 200 microns. The model is shown to naturally predict a size-dependent kinematic hardening behaviour which is responsible for the observed strong size effects. The yield stress at a given averaged plastic strain is shown to follow a power law scaling relation for grain sizes larger than a critical one. The field of plastic deformation is also strongly affected by grain size, whereby micron-size grains lead to the formation of intense slip bands crossing several grains.