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 $\sqrt{s}=$ 7 TeV. The measurement is performed with the electromagnetic calorimeter EMCal and the central tracking detectors, covering a range of $|\eta |<0.27$ in pseudorapidity and a transverse momentum range of $10<{p}_{T}^{\gamma }<60\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}/c$ . The result extends the ${p}_{T}$ coverage of previously published results of the ATLAS and CMS experiments at the same collision energy to smaller ${p}_{T}$ . The measurement is compared to next-to-leading order perturbative QCD calculations and to the results from the ATLAS and CMS experiments. All measurements and theory predictions are in agreement with each other.