Elastic photon-photon scattering can only occur via loop diagrams in the standard model and is naturally suppressed. Unparticle can induce tree-level photon-photon scattering through the operator F_{μν} F^{μν} O_\U for spin-0 unparticle or F_{μα} F^α_ν O^{μν}_\U for spin-2 unparticle. Due to the peculiar CP-conserving phase \exp(-i d_\U π) associated with the s-channel unparticle propagator, its interference effects with the t- and u-channels on the total cross section and the angular distribution are found to be some significance. In addition, we show that the cross sections via unparticle exchange can be substantially larger than the standard model contribution.

8 pages, 2 figures