We conduct a large-scale social media-based study of oral health during the COVID-19 pandemic based on tweets from 9,104 Twitter users across 26 states (with sufficient samples) in the United States for the period between November 12, 2020 and June 14, 2021. To better understand how discussions on different topics/oral diseases vary across the users, we acquire or infer demographic information of users and other characteristics based on retrieved information from user profiles. Women and younger adults (19-29) are more likely to talk about oral health problems. We use the LDA topic model to extract the major topics/oral diseases in tweets. Overall, 26.70% of the Twitter users talk about wisdom tooth pain/jaw hurt, 23.86% tweet about dental service/cavity, 18.97% discuss chipped tooth/tooth break, 16.23% talk about dental pain, and the rest are about tooth decay/gum bleeding. By conducting logistic regression, we find that discussions vary across user characteristics. More importantly, we find social disparities in oral health during the pandemic. Specifically, we find that health insurance coverage rate is the most significant predictor in logistic regression for topic prediction. People from counties with higher insurance coverage tend to tweet less about all topics of oral diseases. People from counties at a higher risk of COVID-19 talk more about tooth decay/gum bleeding and chipped tooth/tooth break. Older adults (50+), who are vulnerable to COVID-19, are more likely to discuss dental pain. To our best knowledge, this is the first large-scale social media-based study to analyze and understand oral health in America amid the COVID-19 pandemic. We hope the findings of our study through the lens of social media can provide insights for oral health practitioners and policy makers.