The purpose of this cross-sectional study was to estimate the proportion of Arkansas residents who were infected with the SARS-CoV-2 virus between May and December 2020 and to assess the determinants of infection. To estimate seroprevalence, a state-wide population-based random-digit dial sample of non-institutionalized adults in Arkansas was surveyed. Exposures were age, sex, race/ethnicity, education, occupation, contact with infected persons, comorbidities, height, and weight. The outcome was past COVID-19 infection measured by serum antibody test. We found a prevalence of 15.1% (95% CI: 11.1%, 20.2%) by December 2020. Seropositivity was significantly elevated among participants who were non-Hispanic Black, Hispanic (prevalence ratio [PRs]:1.4 [95% CI: 0.8, 2.4] and 2.3 [95% CI: 1.3, 4.0], respectively), worked in high-demand essential services (PR: 2.5 [95% CI: 1.5, 4.1]), did not have a college degree (PR: 1.6 [95% CI: 1.0, 2.4]), had an infected household or extra-household contact (PRs: 4.7 [95% CI: 2.1, 10.1] and 2.6 [95% CI: 1.2, 5.7], respectively), and were contacted in November or December (PR: 3.6 [95% CI: 1.9, 6.9]). Our results indicate that by December 2020, one out six persons in Arkansas had a past SARS-CoV-2 infection.