Purpose: The purpose of this study was to investigate cortical tracking of speech (CTS) in adults who stutter (AWS) compared to typically fluent adults (TFAs) to test the involvement of the speech-motor network in tracking rhythmic speech information. Method: Participants' electroencephalogram was recorded while they simply listened to sentences (listening only) or completed them by naming a picture (listening for speaking), thus manipulating the upcoming involvement of speech production. We analyzed speech-brain coherence and brain connectivity during listening. Results: During the listening-for-speaking task, AWS exhibited reduced CTS in the 3- to 5-Hz range (theta), corresponding to the syllabic rhythm. The effect was localized in the left inferior parietal and right pre/supplementary motor regions. Connectivity analyses revealed that TFAs had stronger information transfer in the theta range in both tasks in fronto-temporo-parietal regions. When considering the whole sample of participants, increased connectivity from the right superior temporal cortex to the left sensorimotor cortex was correlated with faster naming times in the listening-for-speaking task. Conclusions: Atypical speech-motor functioning in stuttering impacts speech perception, especially in situations requiring articulatory alertness. The involvement of frontal and (pre)motor regions in CTS in TFAs is highlighted. Further investigation is needed into speech perception in individuals with speech-motor deficits, especially when smooth transitioning between listening and speaking is required, such as in real-life conversational settings.