To choose the appropriate resources for their healthcare needs (e.g., primary care (GP) or emergency department (ED)), patients seeking acute care must self-triage based on their own assessments of symptoms and severity. However, as patients typically lack sufficient medical knowledge, self-triage decisions can often be inaccurate. In response, healthcare and technology companies have been developing and deploying virtual triage tools designed to help patients make better self-triage decisions. To date, however, the operational implications of such tools have not been assessed. This paper therefore develops a queueing game model to investigate the impact of virtual triage in the acute care setting and potential policies to maximize its efficacy. We find that, due to its decentralized nature, when virtual triage excessively recommends emergency (primary) care, it could bring about a decrease in ED (GP) visits. Another important finding is that for any arbitrary self-triage accuracy, the adoption of informative virtual triage can worsen system performance, even when the virtual triage recommendation is reasonably accurate. To unlock the potential operational benefits of virtual triage, we characterize the optimal virtual triage accuracy subjective to the receiver operating characteristic (ROC) curve, and investigate how the optimal accuracy changes as patient compositions or acute care system parameters change, or as the triage capability of virtual triage improves over time.