Accurate measurement of daily infection incidence is crucial to epidemic response. However, delays in symptom onset, testing, and reporting obscure the dynamics of transmission, necessitating methods to remove the effects of stochastic delays from observed data. Existing estimators can be sensitive to model misspecification and censored observations; many analysts have instead used methods that exhibit strong bias. We develop an estimator with a regularization scheme to cope with stochastic delays, which we term the robust incidence deconvolution estimator. We compare the method to existing estimators in a simulation study, measuring accuracy in a variety of experimental conditions. We then use the method to study COVID-19 records in the United States, highlighting its stability in the face of misspecification and right censoring. To implement the robust incidence deconvolution estimator, we release incidental, a ready-to-use R implementation of our estimator that can aid ongoing efforts to monitor the COVID-19 pandemic.