The attributable fraction is a commonly used measure that quantifies the public health impact of an exposure on an outcome. It was originally defined for binary outcomes, but an extension has recently been proposed for right-censored survival time outcomes; the so-called attributable fraction function. A maximum likelihood estimator of the attributable fraction function has been developed, which requires a model for the outcome. In this paper, we derive a doubly robust estimator of the attributable fraction function. This estimator requires one model for the outcome, and one joint model for the exposure and censoring. The estimator is consistent if either model is correct, not necessarily both.