The differential cross section for the inclusive production of isolated prompt photons has been measured as a function of the photon transverse energy ${E}_{T}^{\ensuremath{\gamma}}$ in $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ using data recorded by the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of $2.9\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. Photons are required to have a pseudorapidity $|{\ensuremath{\eta}}^{\ensuremath{\gamma}}|<1.45$ and ${E}_{T}^{\ensuremath{\gamma}}>21\text{ }\text{ }\mathrm{GeV}$, covering the kinematic region $0.006<{x}_{T}<0.086$. The measured cross section is found to be in agreement with next-to-leading-order perturbative QCD calculations.