Transcranial alternating current stimulation (tACS) can non-invasively modulate neuronal activity in the cerebral cortex, in particular at the frequency of the applied stimulation. Such modulation can matter for speech processing, since the latter involves the tracking of slow amplitude fluctuations in speech by cortical activity. tACS with a current signal that follows the envelope of a speech stimulus has indeed been found to influence the cortical tracking and to modulate the comprehension of the speech in background noise. However, how exactly tACS influences the speech-related cortical activity, and how it causes the observed effects on speech comprehension, remains poorly understood. A computational model for cortical speech processing in a biophysically plausible spiking neural network has recently been proposed. Here we extended the model to investigate the effects of different types of stimulation waveforms, similar to those previously applied in experimental studies, on the processing of speech in noise. We assessed in particular how well speech could be decoded from the neural network activity when paired with the exogenous stimulation. We found that, in the absence of current stimulation, the speech-in-noise decoding accuracy was comparable to the comprehension of speech in background noise of human listeners. We further found that current stimulation could alter the speech decoding accuracy by a few percent, comparable to the effects of tACS on speech-in-noise comprehension. Our simulations further allowed us to identify the parameters for the stimulation waveforms that yielded the largest enhancement of speech-in-noise encoding. Our model thereby provides insight into the potential neural mechanisms by which weak alternating current stimulation may influence speech comprehension and allows to screen a large range of stimulation waveforms for their effect on speech processing.