Background Vaccination is considered the best way to prevent the spread of COVID-19 and to prevent the complications of the disease. Nevertheless, no awareness campaigns were conducted in Saudi Arabia until March 1, 2021, when the Vaxzevria, or ChAdOx1 nCoV-19 (AZD1222), vaccine became available. Objectives This study aims to determine the factors that can predict healthcare workers’ acceptance of the COVID-19 vaccine. Methods A cross-sectional study was conducted from July to September 2021, in our university tertiary hospital (King Saud University Medical City [KSUMC]), Riyadh, Saudi Arabia. The study targeted potential participants among healthcare workers at KSUMC. We assessed healthcare workers’ perceptions and beliefs about the COVID-19 vaccine via a questionnaire that was distributed via social media applications such as WhatsApp, Twitter, and Google. Participants were informed about the questionnaire before they filled it out, and they were asked to respond to three screening questions before beginning the main questionnaire. These screening questions ensured that the participants met the inclusion criteria. Included participants were over the age of 18, agreed to answer the questions, and were residents of Saudi Arabia. The participants filled out the self-administered questionnaire. Results A total of 529 participants completed the questionnaires. All participants were vaccinated, 68% were female, 55% were married, 35% had been working for less than five years, and 65% had a bachelor’s degree. More than half of participants had not previously been infected with COVID-19, and most did not interact with COVID-19 patients. More convenient access to the vaccine increased the odds ratio of participant vaccination by 0.39. An increase in the number of vaccinated friends and family members increased the odds ratio of participant vaccination by 0.30. However, COVID- 19 vaccination mandates decreased the odds ratio of participant vaccination by 0.27. The fitted linear regression model explained 32% of the variation observed in the dependent variable, acceptance of the COVID-19 vaccine, and the adjusted R squared was 0.32. The fitted regression model was statistically significant at a 95% confidence interval; the p-value was 0.00001. Conclusion In Saudi Arabia, there is an immense need to increase uptake of the COVID-19 vaccine. This requires encouraging more positive beliefs and attitudes regarding vaccination in general and the COVID-19 vaccine in particular.