This article describes a search for high-mass resonances decaying to a pair of photons using a sample of $20.3$ fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=8$ TeV recorded with the ATLAS detector at the Large Hadron Collider. The data are found to be in agreement with the Standard Model prediction, and limits are reported in the framework of the Randall-Sundrum model. This theory leads to the prediction of graviton states, the lightest of which could be observed at the Large Hadron Collider. A lower limit of $2.66$ ($1.41$) TeV at 95% confidence level is set on the mass of the lightest graviton for couplings of $k/\overline{M}_{\mathrm{Pl}} = 0.1$ ($0.01$).