A measurement is presented of the Z/gamma*->tau tau cross section in pp collisions at root s = 13 TeV, using data recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 2.3 fb(-1). The product of the inclusive cross section and branching fraction is measured to be sigma(pp -> Z/gamma*+X) B(Z/gamma*->tau tau) = 1848 +/- 12 (stat) +/- 67 (syst + lumi) pb, in agreement with the standard model expectation, computed at next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. The measurement is used to validate new analysis techniques relevant for future measurements of tau lepton production. The measurement also provides the reconstruction efficiency and energy scale for tau decays to hadrons + nu(tau) final states, determined with respective relative uncertainties of 2.2 and 0.9%.