We perform a measurement of the CP asymmetry in b-->sgamma decays using a sample of 383 x 10(6) B[over] B events collected by the BABAR detector at the SLAC PEP-II asymmetric B factory. We reconstruct 16 flavor-specific B decay modes containing a high-energy photon and a hadronic system X_(s) containing an s quark. We measure the CP asymmetry to be -0.011+/-0.030(stat)+/-0.014(syst) for a hadronic system mass between 0.6 and 2.8 GeV/c(2).