We report on a search for electronic recoil event rate modulation signatures in the XENON100 data accumulated over a period of 4 yr, from January 2010 to January 2014. A profile likelihood method, which incorporates the stability of the XENON100 detector and the known electronic recoil background model, is used to quantify the significance of periodicity in the time distribution of events. There is a weak modulation signature at a period of 431_{-14}^{+16} day in the low energy region of (2.0-5.8) keV in the single scatter event sample, with a global significance of 1.9σ; however, no other more significant modulation is observed. The significance of an annual modulation signature drops from 2.8σ, from a previous analysis of a subset of this data, to 1.8σ with all data combined. Single scatter events in the low energy region are thus used to exclude the DAMA/LIBRA annual modulation as being due to dark matter electron interactions via axial vector coupling at 5.7σ.