Can a sitting US president hold a reserve military rank?

by yin2lazy

According to this https://en.wikipedia.org/wiki/Harry_S._Truman Harry Truman was in the Army Reserves while being president. How does chain of command work when Commander in Chief is also in the army?

SMIDSY

Form your example, the answer seems to be "yes". My follow up question, though, is can the president can be called up to active duty?