Speech contains pronounced amplitude modulations in the 1–9 Hz range, correlating with the syllabic rate of speech. Recent models of speech perception propose that this rhythmic nature of speech is central to speech recognition and has beneficial effects on language processing. Here, we investigated the contribution of amplitude modulations to the subjective impression listeners have of public speakers. The speech from US presidential candidates Hillary Clinton and Donald Trump in the three TV debates of 2016 was acoustically analyzed by means of modulation spectra. These indicated that Clinton’s speech had more pronounced amplitude modulations than Trump’s speech, particularly in the 1–9 Hz range. A subsequent perception experiment, with listeners rating the perceived charisma of (low-pass filtered versions of) Clinton’s and Trump’s speech, showed that more pronounced amplitude modulations (i.e., more ‘rhythmic’ speech) increased perceived charisma ratings. These outcomes highlight the important contribution of speech rhythm to charisma perception.