Hesitance toward COVID-19 vaccination has greatly decreased over the course of the pandemic in the U.S. However, some populations have lower vaccination rates than the general population. This study was conducted to identify correlates of being fully vaccinated (i.e., having received all doses required to be fully vaccinated) among college students using students’ responses to the 2022 Spring American College Health Association—National College Health Assessment. The surveys were administered in March of 2022. The sample (n = 617) included 18-to-30-year-old students. Firth logistic regression models were performed that controlled for age, sex assigned at birth, and food security (at a 5% significance level). The model-assisted results indicated that being a member of sexual and gender minority communities, being a graduate student, and being concerned about someone close getting COVID-19 were positively associated with being fully vaccinated, while current use of any tobacco product and current use of e-cigarettes were negatively associated with being fully vaccinated (all p-values < 0.05). In addition, the percentage of fully vaccinated students was higher among transgender/gender non-binary students (95%) than among cisgender men and women (85–87%), and among sexual minority groups (93–97%) than among heterosexual/straight students (82%). Among the racial/ethnic groups considered, the percentage of fully vaccinated students was lowest among non-Hispanic Black/African American students (77%), but the racial/ethnic differences were not statistically significant (at 5% level). The study points to a critical need for development and implementation of tailored vaccination campaigns to help students from diverse communities, including tobacco users, make informed decisions and become fully vaccinated.