The elastic resonance scattering of ^12C+p has been studied in inverse kinematics via a novel thicktarget method at GIRAFFE facility of HI-13 tandem accelerator laboratory, Beijing. The recoil protons weremeasured by a AE-E counter telescope based on a large area double-sided silicon strip detector at laboratoryangles around θ0 = 15^o. The excitation function for ^12C(p,p) elastic scattering has been obtained over a wideenergy range of Ec.m. =0.31-3.45 MeV, which was explained quite well by the R-matrix calculation with known resonance parameters of the first three levels in ^13N nucleus. Thus it is demonstrated that the present setup can be directly applied to the study of elastic resonance scattering with secondary radioactive beams.