A measurement of the cross section for the production of isolated prompt photons in p p collisions at a center-of-mass energy s= 7 TeV is presented. The results are based on an integrated luminosity of 4.6 fb− 1 collected with the ATLAS detector at the LHC. The cross section is measured as a function of photon pseudorapidity η γ and transverse energy E T γ in the kinematic range 100≤ E T γ< 1000 GeV and in the regions| η γ|< 1.37 and 1.52≤| η γ|< 2.37. The results are compared to leading-order parton-shower Monte Carlo models and next-to-leading-order perturbative QCD calculations. Next-to-leading-order perturbative QCD calculations agree well with the measured cross sections as a function of E T γ and η γ.