Textured transparent conductors are widely used in thin-film silicon solar cells. They lower the reflectivity at interfaces between different layers in the cell and/or cause an increase in the path length of photons in the Si absorber layer, which both result in an increase in the number of absorbed photons and, consequently, an increase in short-circuit current density (Jsc) and cell efficiency. Through optical simulations, we recently obtained strong indications that texturing of the transparent conductor in copper indium gallium (di-)selenide (CIGS) solar cells is also optically advantageous. Here, we experimentally demonstrate that the Jsc and efficiency of CIGS solar cells with an absorber layer thickness (dCIGS) of 0.85 μm, 1.00 μm and 2.00 μm increase through application of a moth-eye textured resist with a refractive index that is sufficiently similar to AZO (nresist = 1.792 vs. nAZO = 1.913 at 633 nm) to avoid large optical losses at the resist-AZO interface. On average, Jsc increases by 7.2%, which matches the average reduction in reflection of 7.0%. The average relative increase in efficiency is slightly lower (6.0%). No trend towards a larger relative increase in Jsc with decreasing dCIGS was observed. Ergo, the increase in Jsc can be fully explained by the reduction in reflection, and we did not observe any increase in Jsc based on an increased photon path length.