A measurement of the cross section for the inclusive production of isolated prompt photons in $pp$ collisions at a center-of-mass energy $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ is presented. The measurement covers the pseudorapidity ranges $|{\ensuremath{\eta}}^{\ensuremath{\gamma}}|<1.37$ and $1.52\ensuremath{\le}|{\ensuremath{\eta}}^{\ensuremath{\gamma}}|<1.81$ in the transverse energy range $15\ensuremath{\le}{E}_{\mathrm{T}}^{\ensuremath{\gamma}}<100\text{ }\text{ }\mathrm{GeV}$. The results are based on an integrated luminosity of $880\text{ }\text{ }{\mathrm{nb}}^{\ensuremath{-}1}$, collected with the ATLAS detector at the Large Hadron Collider. Photon candidates are identified by combining information from the calorimeters and from the inner tracker. Residual background in the selected sample is estimated from data based on the observed distribution of the transverse isolation energy in a narrow cone around the photon candidate. The results are compared to predictions from next-to-leading-order perturbative QCD calculations.