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 unbinned profile likelihood analysis to identify any periodicity up to 500 days. We find a global significance of less than 1σ for all periods, suggesting no statistically significant modulation in the data. While the local significance for an annual modulation is 2.8σ, 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 weakly interacting massive particles to electrons is excluded at 4.8σ.