Wrong!
No, they have satellites and launch vehicles like the Delta IV and Atlas V. AF bases are routinely used to launch and operate satellites.
Satellites are used extensively for satellite aided navigation, meteorological observation, visual & radar observation of enemy assets and communication.
Meanwhile, the nuclear ballistic missiles travel through space. All ballistic missiles starting with the Nazi V-2 do this; they launch into space then fall onto the target! This makes a ballistic missile a type of primitive spacecraft.
The Space Shuttle was also originally designed to USAF specifications, but it was ultimately used only by NASA. It turns out the USAF prefers big dumb boosters. This is why the shuttle cannot go to the Moon; the USAF has no business on the Moon, so it's design sacrifices long duration flight & high speed re-entry in favor of cross range maneuverability post-reentry that the AF desired.
Back in the 80s the USAF also came up with an F-15 launched anti-satellite missile. They even popped one satellite in testing in the early 80s. It is called the ASM-135.
They did not maintain this capability however, and some ASM-135s now reside in museums.