Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice gauge theories in table-top experiments. However, the realization of non-Abelian models remains challenging. Here, we employ a coherent quantum control scheme to enforce non-Abelian gauge invariance, and discuss this idea in detail for a one dimensional SU(2) lattice gauge system. Finally, we comment on how to extend our scheme to other non-Abelian gauge symmetries and higher spatial dimensions, which summarized, provides a promising route for the quantum simulation of non-Abelian lattice gauge theories.