The Soyuz rocket blasted off at 04:14:25 GMT from the Baikonur cosmodrome in Kazakhstan.
Three cosmonauts - Russia's Mikhail Tyurin, American Rick Mastracchio and Koici Wakata from Japan - are taking the torch to the ISS, which it is due to reach in six hours.
The Olympic symbol will be handed over to fellow cosmonauts Oleg Kotov and Sergei Ryazansky, who are already on the orbiting station, when they go on the spacewalk on Saturday.