This paper describes the calibration procedure for the drift tubes of the CMS barrel muon system and reports the main results obtained with data collected during a high statistics cosmic ray data-taking period. The main goal of the calibration is to determine, for each drift cell, the minimum time delay for signals relative to the trigger, accounting for the drift velocity within the cell. The accuracy of the calibration procedure is influenced by the random arrival time of the cosmic muons relative to the LHC clock cycle. A more refined analysis of the drift velocity was performed during the offline reconstruction phase, which takes into account this feature of cosmic ray events.