Transcranial alternating current stimulation (tACS) at 10 Hz has been shown to modulate spatial attention. However, the frequency-specificity and the oscillatory changes underlying this tACS effect are still largely unclear. Here, we applied high-definition tACS at individual alpha frequency (IAF), two control frequencies (IAF+/-2Hz) and sham to the left posterior parietal cortex and measured its effects on visuospatial attention performance and offline alpha power (using electroencephalography, EEG). We revealed a behavioural and electrophysiological stimulation effect relative to sham for IAF but not control frequency stimulation conditions: there was a leftward lateralization of alpha power for IAF tACS, which differed from sham for the first out of three minutes following tACS. At a high value of this EEG effect (moderation effect), we observed a leftward attention bias relative to sham. This effect was task-specific, i.e., it could be found in an endogenous attention but not in a detection task. Only in the IAF tACS condition, we also found a correlation between the magnitude of the alpha lateralization and the attentional bias effect. Our results support a functional role of alpha oscillations in visuospatial attention and the potential of tACS to modulate it. The frequency-specificity of the effects suggests that an individualization of the stimulation frequency is necessary in heterogeneous target groups with a large variation in IAF.