Transcranial alternating current stimulation (tACS) can be used to study causal contributions of oscillatory brain mechanisms to cognition and behavior. For instance, individual alpha frequency (IAF) tACS was reported to enhance alpha power and impact visuospatial attention performance. Unfortunately, such results have been inconsistent and difficult to replicate. In tACS, stimulation generally involves one frequency, sometimes individually calibrated to a peak value observed in an M/EEG power spectrum. Yet, the ‘peak’ actually observed in such power spectra often contains a broader range of frequencies, raising the question whether a biologically calibrated tACS protocol containing this fuller range of alpha-band frequencies might be more effective. Here, we introduce ‘Broadband-alpha-tACS’, a complex individually calibrated electrical stimulation protocol. We band-pass filtered left posterior resting-state EEG data around the IAF (± 2 Hz), and converted that time series into an electrical waveform for tACS stimulation of that same left posterior parietal cortex location. In other words, we stimulated a brain region with a ‘replay’ of its own alpha-band frequency content, based on spontaneous activity. Within-subjects (N = 24), we compared to a sham tACS session the effects of broadband-alpha tACS, power-matched spectral inverse (‘alpha-removed’) control tACS, and individual alpha frequency (IAF) tACS, on EEG alpha power and performance in an endogenous attention task previously reported to be affected by alpha tACS. Broadband-alpha-tACS significantly modulated attention task performance (i.e., reduced the rightward visuospatial attention bias in trials without distractors, and reduced attention benefits). Alpha-removed tACS also reduced the rightward visuospatial attention bias. IAF-tACS did not significantly modulate attention task performance compared to sham tACS, but also did not statistically significantly differ from broadband-alpha-tACS. This new broadband-alpha-tACS approach seems promising, but should be further explored and validated in future studies.