A search for a nonzero neutrino magnetic moment has been conducted using 1496 live days of solar neutrino data from Super-Kamiokande-I. Specifically, we searched for distortions to the energy spectrum of recoil electrons arising from magnetic scattering due to a nonzero neutrino magnetic moment. In the absence of a clear signal, we found micro(nu)</=(3.6x10(-10))micro(B) at 90% C.L. by fitting to the Super-Kamiokande day-night spectra. The fitting took into account the effect of neutrino oscillation on the shapes of energy spectra. With additional information from other solar neutrino and KamLAND experiments constraining the oscillation region, a limit of micro(nu)</=(1.1x10(-10))micro(B) at 90% C.L. was obtained.