  This paper presents a measurement of the W^+W^- production cross section in
pp collisions at sqrt{s}=7 TeV. The leptonic decay channels are analyzed using
data corresponding to an integrated 4.6 fb-1 collected with the ATLAS detector
at the Large Hadron Collider. The W^+W^- production cross section sigma(pp ->
W^+W^-+X) is measured to be 51.9 +- 2.0 (stat) +- 3.9 (syst) +- 2.0 (lumi) pb,
compatible with the Standard Model prediction of 44.7 +2.1 -1.9 pb. A
measurement of the normalized fiducial cross section as a function of the
leading lepton transverse momentum is also presented. The reconstructed
transverse momentum distribution of the leading lepton is used to extract
limits on anomalous WWZ and WWgamma couplings.
