Orienting spatial attention has been associated with interhemispheric asymmetry of power in the α- and γ-band. Specifically, increased α-power has been linked to the inhibition of unattended sensory streams (e.g. the unattended visual field), while increased γ-power is associated with active sensory processing. Here, we aimed to differentially modulate endogenous and exogenous visual-spatial attention using transcranial alternating current stimulation (tACS). In a single-blind, within-subject design, participants performed several blocks of a spatial cueing task comprised of endogenous and exogenous cues while receiving lateralized α- or γ-tACS or no stimulation over left or right occipital-parietal areas. We found a significant, differential effect of α- and γ-tACS on endogenous (top-down) spatial attention but not on exogenous (bottom-up) attention. The effect was specific to tACS applied to the left hemisphere and driven by a modulation of attentional disengagement and re-orientation as measured during invalid trials. Our results indicate a causal role of α-/γ-oscillations for top-down (endogenous) attention. They may further suggest a left hemispheric dominance in controlling interhemispheric α-/γ-power asymmetry. The absence of an effect on exogenous attention may be indicative of a differential role of α-/γ-oscillations during different attention types or spatially distinct attentional subsystems.