  We show how to construct a tensor network representation of the path integral
for reduced staggered fermions coupled to a non-abelian gauge field in two
dimensions. The resulting formulation is both memory and computation efficient
because reduced staggered fermions can be represented in terms of a minimal
number of tensor indices while the gauge sector can be approximated using
Gaussian quadrature with a truncation. Numerical results obtained using the
Grassmann TRG algorithm are shown for the case of $SU(2)$ lattice gauge theory
and compared to Monte Carlo results.
