During the COVID-19 pandemic, social media has become an emerging platform for the public to find information, share opinions, and seek coping strategies. Vaccination, one of the most effective public health interventions to control the COVID-19 pandemic, has become the focus of public online discussions. Several studies have demonstrated that social bots actively involved in topic discussions on social media and expressed their sentiments and emotions, which affected human users. However, it is unclear whether social bots’ sentiments affect human users’ sentiments of COVID-19 vaccines. This study seeks to scrutinize whether the sentiments of social bots affect human users’ sentiments of COVID-19 vaccines. The work identified social bots and built an innovative computational framework, i.e., the BERT-CNN sentiment analysis framework, to classify tweet sentiments at the three most discussed stages of COVID-19 vaccines on Twitter from December 2020 to August 2021, thus exploring the impacts of social bots on online vaccine sentiments of humans. Then, the Granger causality test was used to analyze whether there was a time-series causality between the sentiments of social bots and humans. The findings revealed that social bots can influence human sentiments about COVID-19 vaccines. Their ability to transmit the sentiments on social media, whether in the spread of positive or negative tweets, will have a corresponding impact on human sentiments.