Several recent studies have used transcranial alternating current stimulation (tACS) to demonstrate a causal role of neural oscillatory activity in speech processing. In particular, it has been shown that the ability to understand speech in a multi-speaker scenario or background noise depends on the timing of speech presentation relative to simultaneously applied tACS. However, it is possible that tACS did not change actual speech perception but rather auditory stream segregation. In this study, we tested whether the phase relation between tACS and the rhythm of degraded words, presented in silence, modulates word report accuracy. We found strong evidence for a tACS-induced modulation of speech perception, but only if the stimulation was applied bilaterally using ring electrodes (not for unilateral left hemisphere stimulation with square electrodes). These results were only obtained when data were analyzed using a statistical approach that was identified as optimal in a previous simulation study. The effect was driven by a phasic disruption of word report scores. Our results suggest a causal role of neural entrainment for speech perception and emphasize the importance of optimizing stimulation protocols and statistical approaches for brain stimulation research.