Introduction The increasing incidence of acute appendicitis in sub-Saharan Africa emphasizes the need for accurate and reliable diagnostic tools. However, the variability in the diagnostic performance of computed tomography for suspected acute appendicitis coupled with comparatively higher negative appendectomy rates in this setting highlight a possible concern regarding the diagnostic accuracy. This study evaluated the diagnostic accuracy of a computed tomography scan for suspected acute appendicitis at the emergency department in Tanzania. Methods A retrospective diagnostic accuracy study was conducted from July to October 2020. All patients above 14 years of age who presented at the emergency department with right iliac fossa abdominal pain of fewer than ten days and underwent computed tomography for suspected acute appendicitis were evaluated, and the Alvarado score was computed. Histological diagnosis and clinical follow-up of 14 days were considered the reference standard. Ethical clearance was sought from the Aga Khan University Ethical review committee. Results 176 patients were included in this study. The sensitivity, specificity, and diagnostic accuracy were 100% (95% CI 91.8–100), 96.9% (95% CI 92.2–99.1), and 96.9% (95% CI 93.1–98.3), respectively. The mean Alvarado score in those without acute appendicitis was 4 (95% CI 3.7–4.3) compared to a mean score of 6.6 (95% CI 6.0–7.2) amongst those with acute appendicitis. The area under the receiver operator characteristics curve of computed tomography was 98.4%, and that of the Alvarado score was 84.1%. Conclusions The diagnostic performance of computed tomography in this study is similar to that established elsewhere. However, the Alvarado score is not routinely used for the initial screening of suspected acute appendicitis patients. A threshold of Alvarado score of 4 as a guide to conduct computed tomography for suspected acute appendicitis would have decreased computed tomography use by 50%, and missed 4 cases. Implementation studies that address Alvarado score use should be conducted.