There are three ICBM based rockets on the schedule: Mercury, Titan II, and Soyuz. All three of these rockets can put a dummy explosive module payload into orbit with careful fuel management. Adding a tug module as second stage makes it much easier to achieve orbit.
Mercury
Titan II
The Gemini Program was also based on ICBM technology with the Titan II. This technology was used in rockets for forty years with the last launch in 2003.
Soyuz
The modern Soyuz was developed from the R-7 rocket. The first R-7 was designed to be used as an ICBM. Derivatives of the R-7 hold a huge place in space history. It was used to launch the first artificial satellite, Sputnik, and the first human in space, Yuri Gagarin. Derivatives of it are still in use today.