We present the first direct measurement of the top-quark mass using tt ̄ events decaying in the hadronic τ+jets decay channel. Using data corresponding to an integrated luminosity of 2.2 fb−1 collected by the CDF II detector in pp ̄ collisions at √s=1.96 TeV at the Fermilab Tevatron, we measure the tt ̄ cross section, σtt ̄, and the top-quark mass, Mtop. We extract Mtop from a likelihood based on per-event probabilities calculated with leading-order signal and background matrix elements. We measure σtt ̄=8.8±3.3(stat)±2.2(syst) pb and Mtop=172.7±9.3(stat)±3.7(syst) GeV/c2.