The differential cross section, d sigma/dt, for rho(0) meson photoproduction on the proton above the resonance region was measured up to a momentum transfer -t = 5 GeV2 using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The rho(0) channel was extracted from the measured two charged-pion cross sections by fitting the pi(+)pi(-) and p pi(+) invariant masses. The low momentum transfer region shows the typical diffractive pattern expected from Reggeon exchange. The flatter behavior at large -t cannot be explained solely in terms of QCD-inspired two-gluon exchange models. The data indicate that other processes, like quark interchange, are important to fully describe rho photoproduction.