The production cross section of inclusive isolated photons has been measured by the ALICE experiment at the CERN LHC in pp collisions at a centre-of-momentum energy of root s = 7 TeV. The measurement is performed with the electromagnetic calorimeter EMCal and the central tracking detectors, covering a range of vertical bar eta vertical bar <0.27 in pseudorapidity and a transverse momentum range of 10 <p(T)(gamma) <60 GeV/c. The result extends the pT coverage of previously published results of the ATLAS and CMS experiments at the same collision energy to smaller pT. The measurement is compared to next-to-leading order perturbative QCD calculations and to the results from the ATLAS and CMS experiments. Allmeasurements and theory predictions are in agreement with each other.