  We have searched for periodic variations of the electronic recoil event rate
in the (2-6) keV energy range recorded between February 2011 and March 2012
with the XENON100 detector, adding up to 224.6 live days in total. Following a
detailed study to establish the stability of the detector and its background
contributions during this run, we performed an un-binned profile likelihood
analysis to identify any periodicity up to 500 days. We find a global
significance of less than 1 sigma for all periods suggesting no statistically
significant modulation in the data. While the local significance for an annual
modulation is 2.8 sigma, the analysis of a multiple-scatter control sample and
the phase of the modulation disfavor a dark matter interpretation. The
DAMA/LIBRA annual modulation interpreted as a dark matter signature with
axial-vector coupling of WIMPs to electrons is excluded at 4.8 sigma.
