During autumn 2008, the Silicon Strip Tracker was operated with the full CMS experiment in a comprehensive test, in the presence of the 3.8 T magnetic field produced by the CMS superconducting solenoid. Cosmic ray muons were detected in the muon chambers and used to trigger the readout of all CMS sub-detectors. About 15 million events with a muon in the tracker were collected. The efficiency of hit and track reconstruction were measured to be higher than 99% and consistent with expectations from Monte Carlo simulation. This article details the commissioning and performance of the Silicon Strip Tracker with cosmic ray muons.