Taiwan has been a world leader in controlling the spread of SARS-CoV-2 during the COVID-19 pandemic. Recently, the Taiwan Government launched its COVID-19 tracing app, ‘Taiwan Social Distancing App’; however, the effectiveness of this tracing app depends on its acceptance and uptake among the general population. We measured the acceptance of three hypothetical tracing technologies (telecommunication network tracing, a government app, and the Apple and Google Bluetooth exposure notification system) in four nationally representative Taiwanese samples. Using Bayesian methods, we found a high acceptance of all three tracking technologies, with acceptance increasing with the inclusion of additional privacy measures. Modeling revealed that acceptance increased with the perceived technology benefits, trust in the providers’ intent, data security and privacy measures, the level of ongoing control, and one’s level of education. Acceptance decreased with data sensitivity perceptions and a perceived low policy compliance by others among the general public. We consider the policy implications of these results for Taiwan during the COVID-19 pandemic and in the future.