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The rapid cycling synchrotron (RCS) of the China Spallation Neutron Source (CSNS) employs painting injection to achieve a uniform beam distribution and to suppress the space charge effect. In the painting injection, a mismatch between the injection and the circulating beam orbit can cause nonuniform beam distribution and larger emittance, which may lead to beam loss. To match the injection beam orbit and the circulating beam orbit, it is necessary to identify the injection beam orbit relative to the circulating beam orbit at the injection point. However, the relative injection beam orbit is hard to measure directly. Theoretically, the relative injection beam orbit can be deduced from the turn-by-turn beam position of a single-turn injected beam, but in the RCS of CSNS, the intensity of a single-turn injected beam is too low to measure with a sufficient signal-noise ratio using a beam position monitor. In this paper, two effective methods based on multiturn injection and turn-by-turn beam position data are given to perform the match between the injection and the circulating beam orbit. Simulation results and practical application during the beam commissioning of the RCS of CSNS show the validity of the methods.