A measurement of the cross section for the inclusive production of isolated prompt photons in proton-proton collisions at a centre-of-mass energy of root s = 8 TeV is presented. The measurement covers the pseudorapidity ranges vertical bar eta(gamma)vertical bar < 1.37 and 1.56 aecurrency sign vertical bar eta(gamma)vertical bar < 2.37 in the transverse energy range 25 < E-T(gamma) < 1500 GeV. The results are based on an integrated luminosity of 20.2 fb(-1), recorded by the ATLAS detector at the LHC. Photon candidates are identified by combining information from the calorimeters and the inner tracker. The background is subtracted using a data-driven technique, based on the observed calorimeter shower-shape variables and the deposition of hadronic energy in a narrow cone around the photon candidate. The measured cross sections are compared with leading-order and next-to-leading order perturbative QCD calculations and are found to be in a good agreement over ten orders of magnitude.