ABSTRACT Digital contact tracing (DCT) has emerged as a promising tool for controlling infectious disease outbreaks, yet its adoption has been hampered by widespread privacy concerns. Prior research studies mainly rely on privacy calculus theory. We extend this view by integrating agency theory to explain how delegating sensitive data to government authorities generates anticipatory concerns about misuse. Building upon the social risk concept introduced in earlier DCT studies, we theoretically refine and contextualize surveillance drift concern , defined as an anticipatory belief that personal data collected for legitimate and time‐limited public health purposes may be repurposed, prolonged, or expanded once the original emergency ends. We model this concern as a key mechanism linking privacy uncertainty and societal utility to DCT acceptance and examine how public health crisis‐induced anxiety moderates these effects. A scenario‐based experiment ( N = 315) supports our model. Our findings advance theoretical understanding of how DCT acceptance emerges under conditions of delegation, uncertainty and crisis governance, while offering actionable insights for designing and communicating trustworthy digital public health systems.