This Letter presents a search for tb resonances in 1.04 fb(-1) of LHC proton-proton collision data collected by the ATLAS detector at a center-of-mass energy of 7 TeV. Events with a lepton, missing transverse momentum, and two jets are selected and the invariant mass of the corresponding final state is reconstructed. The search exploits the shape of the tb invariant mass distribution compared to the expected standard model backgrounds. The model of a right-handed W'(R) with standard model-like couplings is chosen as the benchmark model for this search. No statistically significant excess of events is observed in the data, and upper limits on the cross section times the branching ratio of W'(R) resonances at 95% C.L. lie in the range of 6.1-1.0 pb for W'(R) masses ranging from 0.5 to 2.0 TeV. These limits are translated into a lower bound on the allowed right-handed W'(R) mass, giving mW'(R) > 1.13 TeV at 95% C.L.