Conversational agents (CAs) are emerging as potential solutions in healthcare for triage, symptom checking, and patient guidance. However, despite technological advances, the acceptance of such systems continues to remain low. Along with functional aspects, the interaction layer plays an important role in enhancing user trust and acceptance. Building on this, the study investigates whether rhetorical persuasive communication styles can improve users’ perceived trust and acceptance of healthcare CAs. Based on Aristotelian rhetoric, three conversational styles were designed—Ethos (credibility), Pathos (emotional appeal), and Logos (rationality) and implemented in a Wizard-of-Oz within-subject experiment (N = 36) along with a neutral Baseline style across four non-critical medical scenarios. Results show that communication style significantly influenced system acceptance but not trust, suggesting that trust in healthcare chatbots is probably based on reliability and competence than conversational style. Ethos and Pathos were perceived as most useful; Logos was ranked highest while Baseline was least preferred. Further analyses revealed that user traits did not moderate the effects on trust and system acceptance.