This Letter reports a measurement of the W W production cross section in root s = 7 TeV pp collisions using data corresponding to an integrated luminosity of 1.02 fb(-1) collected with the ATLAS detector. Using leptonic decays of oppositely charged W bosons, the total measured cross section is sigma (pp -> W W) = 54.4 +/- 4.0 (stat.) +/- 3.9 (syst.) +/- 2.0 (lumi.) pb, consistent with the Standard Model prediction of sigma (pp -> W W)= 44.4 +/- 2.8 pb. Limits on anomalous electroweak triple-gauge couplings are extracted from a fit to the transverse-momentum distribution of the leading charged lepton in the event. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.