We present a measurement of the isolated direct photon cross section using 36.1 pb−1 of pp collision data at √s = 7 TeV collected with the Compact Muon Solenoid (CMS) experiment during the 2010 physics run of the CERN Large Hadron Collider (LHC). The measurement is performed on events where the pho- ton candidate converts into an e+e− pair in the material of the inner tracking system. The transverse momentum of the conversion track pair is compared with the transverse energy measured in the CMS electromagnetic calorimeter (ECAL), and is then used to subtract the background due to e.g. π0 → γγ decays. We measure the photon cross section over a range of photon transverse momentum and pseudorapidity and find that it agrees with the predictions of perturbative quantum chromodynamics (QCD) calculations.