  A search has been made for sinusoidal periodic variations in the $^8$B solar
neutrino flux using data collected by the Sudbury Neutrino Observatory over a
4-year time interval. The variation at a period of one year is consistent with
modulation of the $^8$B neutrino flux by the Earth's orbital eccentricity. No
significant sinusoidal periodicities are found with periods between 1 day and
10 years with either an unbinned maximum likelihood analysis or a Lomb-Scargle
periodogram analysis. The data are inconsistent with the hypothesis that the
results of the recent analysis by Sturrock et al., based on elastic scattering
events in Super-Kamiokande, can be attributed to a 7% sinusoidal modulation of
the total $^8$B neutrino flux.
