We have performed a search for new particles which decay to two photons using 1.2  fb−1 of integrated luminosity from pp collisions at s√=1.96  TeV collected using the CDF II detector at the Fermilab Tevatron. We find the diphoton mass spectrum to be in agreement with the standard model expectation, and set limits on the cross section times branching ratio for the Randall-Sundrum graviton, as a function of diphoton mass. We subsequently derive lower limits for the graviton mass of 230  GeV/c2 and 850  GeV/c2, at the 95% confidence level, for coupling parameters (k/MPl) of 0.01 and 0.1, respectively.