Toric Fano varieties build an important example class in algebraic geometry as their high symmetry allows to describe them in a purely combinatorial manner via the so-called Fano polytopes. The anticanonical complex is a combinatorial tool that was invented to extend the features of the Fano polytope to wider classes of varieties. In this talk we show how the anticanonical complex can be used to read off the Gorenstein index of Fano varieties with torus action of complexity one in full analogy to the toric Fano polytope.