The production of hard photons in hadronic collisions is studied using Soft-Collinear Effective Theory (SCET). This is the first application of SCET to a physical cross section involving energetic partons in more than two directions. A factorization formula is derived which manifests a number of new features, such as a non-trivial interplay between the angular dependence of the hard and soft functions, multiple partonic channels, and the appearance of a gluon jet function. The relevant hard, jet and soft functions are computed to one loop and their anomalous dimensions are determined to three loops. The final resummed inclusive direct photon distribution is valid to next-to-next-to-leading logarithmic order (NNLL), one order beyond previous work. The result is improved by including non-logarithmic terms and photon isolation cuts through matching, and compared to Tevatron data and to fixed order results at the Tevatron and the LHC. The resummed cross section has a significantly smaller theoretical uncertainty than the next-to-leading fixed-order result, particularly at high transverse momentum.