Measuring the body's response to treatments for circadian dysfunction, as well as optimizing the daily timing of treatments for other health conditions, requires a method for accurately tracking the state of a person's circadian clock. We used a recently developed method called ZeitZeiger to predict circadian time (CT, time of day according to the circadian clock) from genome-wide gene expression in human blood. In 10-fold cross-validation on 498 samples from 60 individuals across three publicly available datasets, ZeitZeiger predicted CT with a median absolute error of 2.1 h. The predictor trained on all 498 samples used 15 genes, only two of which are part of the core circadian clock. We then extended ZeitZeiger to make predictions for groups of samples and to personalize predictions using samples from only the respective individual. Each of these strategies improved accuracy by ~20%. Our results are an important step towards precision circadian medicine.