We report a measurement of the cross section for the process γγ → π + π − at invariant masses 500 MeV/ c 2 < m ππ <2000 MeV/ c 2 . A value for the radiative width of the f(1270) tensor meson Γ f→ γγ = 3.6 ± 0.3 ± 0.5 KeV (helicity λ = 2) has been obtained from a fit to the observed ππ mass spectrum.