Artificial intelligence (AI) has given us social robots that interact with us in everyday life. As chatbots, they are sometimes the first point of entry for contacting a brand. Trends have emerged with human-like social media robot influencers (SMRs) promoting products and services. The literature on this subject is incomplete, so this study aims to mobilize source credibility theory to analyze the influence of individuals' perceptions of SMRs on attitudes toward their use. The influence of anthropomorphism on attitude is investigated, and the relationship is analyzed between attitudes on purchase intention for products promoted by both SMRs and e-word-of-mouth. Finally, the impact of gender and native continent as moderators is controlled. Using a quantitative method, a survey based on existing scales was scripted, and a total sample of 300 digital natives (born after 1980) was collected worldwide. The results were analyzed using the partial least approach and SmartPLS4 software. Our findings reveal the importance of trustworthiness, expertise, physical attractiveness, content attractiveness, and anthropomorphic appearance. However, similarities between influencers and followers have no impact on attitudes toward the use of SMRs. Finally, the theory of source credibility is shown to be enriched by anthropomorphism, and the moderating effect of gender and native continent is demonstrated.