Transcranial alternating current stimulation with the speech envelope can modulate the comprehension of speech in noise. The modulation stems from the theta- but not the delta-band portion of the speech envelope, and likely reflects the entrainment of neural activity in the theta frequency band, which may aid the parsing of the speech stream. The influence of the current stimulation on speech comprehension can vary with the time delay between the current waveform and the audio signal. While this effect has been investigated for current stimulation based on the entire speech envelope, it has not yet been measured when the current waveform follows the theta-band portion of the speech envelope. Here, we show that transcranial current stimulation with the speech envelope filtered in the theta frequency band improves speech comprehension as compared to a sham stimulus. The improvement occurs when there is no time delay between the current and the speech stimulus, as well as when the temporal delay is comparatively short, 90 ms. In contrast, longer delays, as well as negative delays, do not impact speech-in-noise comprehension. Moreover, we find that the improvement of speech comprehension at no or small delays of the current stimulation is consistent across participants. Our findings suggest that cortical entrainment to speech is most influenced through current stimulation that follows the speech envelope with at most a small delay. They also open a path to enhancing the perception of speech in noise, an issue that is particularly important for people with hearing impairment.