Working memory (WM) and short-term memory (STM) supposedly rely on the phase-amplitude coupling (PAC) of neural oscillations in the theta and gamma frequency ranges. The ratio between the individually dominant gamma and theta frequencies is believed to determine an individual's memory capacity. The aim of this study was to establish a causal relationship between the gamma/theta ratio and WM/STM capacity by means of transcranial alternating current stimulation (tACS). To achieve this, tACS was delivered at a frequency below the individual theta frequency. Thereby the individual ratio of gamma to theta frequencies was changed, resulting in an increase of STM capacity. Healthy human participants (N = 33) were allocated to two groups, one receiving verum tACS, the other underwent a sham control protocol. The electroencephalogram (EEG) was measured before stimulation and analyzed with regard to the properties of PAC between theta and gamma frequencies to determine individual stimulation frequencies. After stimulation, EEG was recorded again in order to find after-effects of tACS in the oscillatory features of the EEG. Measures of STM and WM were obtained before, during and after stimulation. Frequency spectra and behavioral data were compared between groups and different measurement phases. The tACS- but not the sham stimulated group showed an increase in STM capacity during stimulation. WM was not affected in either groups. An increase in task-related theta amplitude after stimulation was observed only for the tACS group. These augmented theta amplitudes indicated that the manipulation of individual theta frequencies was successful and caused the increase in STM capacity.