In this work, we explore the microstructural properties that give rise to the plastic anisotropy observed in columnar-grained, nano-twinned Cu. A statistical model for randomly varying source lengths within the grain boundaries of the nanostructure is developed. The model is used to calculate a corresponding critical resolved shear stress for emitting dislocations within a twin lamella on slip systems lying either parallel or inclined from its twin boundary. By incorporating this model into a 3D crystal plasticity finite element model, we can link texture and slip patterns within the twin lamella to anisotropy in the plastic deformation behavior. The model achieves good agreement with flow stress strain evolution and yield data collected over many studies. We show that reducing twin thickness can increase plastic anisotropy as a result of the increase in mean stress to emit dislocations. It is also found that finer twins can lower strain hardening as a consequence of a lower statistical variation in the emission stress.