Transcranial electrical stimulation has widespread clinical and research applications, yet its effect on ongoing neural activity in humans is not well established. Previous reports argue that transcranial alternating current stimulation (tACS) can entrain and enhance neural rhythms related to memory, but the evidence from non-invasive recordings has remained inconclusive. Here, we measure endogenous spindle and theta activity intracranially in humans during low-frequency tACS and find no stable entrainment of spindle power during non-REM sleep, nor of theta power during resting wakefulness. As positive controls, we find robust entrainment of spindle activity to endogenous slow-wave activity in 66% of electrodes as well as entrainment to rhythmic noise-burst acoustic stimulation in 14% of electrodes. We conclude that low-frequency tACS at common stimulation intensities neither acutely modulates spindle activity during sleep nor theta activity during waking rest, likely because of the attenuated electrical fields reaching the cortical surface.