Quadratic detection in linear mesoscopic transport systems produces cross terms that can be viewed as interference signals reflecting statistical properties of charge carriers. In electronic systems these cross-term interferences arise from exchange effects due to Pauli principle. Here we demonstrate fermionic Hanbury Brown and Twiss (HBT) exchange phenomena due to indistinguishability of charge carriers in a diffusive graphene system. These exchange effects are verified using current-current cross-correlations in combination with regular shot noise (autocorrelation) experiments at microwave frequencies. Our results can be modeled using semiclassical analysis for a square-shaped metallic diffusive conductor, including contributions from contact transparency. The experimentally determined HBT exchange factor values lie between the calculated ones for coherent and hot electron transport.