At the moment, it makes no sense.. We can't put a man into orbit without buying a ticket on a Russian launch (technically I guess we could also buy a ride from China.) That being the case a "Space Force" that is co-equal with the other service branches is not needed.
There may well be efficiencies to be had in pooling responsibility for the various satellite assets run by the existing services under some unified command. That might require a few thousand personnel, possibly fewer. Not seeing a need for a separate military service branch there.
I'm also not seeing much of a mission for such a service, if it existed. Note that the USAF started a Man in Space program about the time Project Mercury was getting underway, and at one point planned to use Gemini spacecraft (and future modifications of that craft) to carry crews to and from space station(s). But they quickly came to the conclusion that there was actually nothing for their personnel to do -- the only real mission was espionage, and that was done more cheaply by satellites. The Soviets used every other Salyut station as a military espionage station, but they gave that up, too, as satellite tech enabled unmanned orbital assets to take over the job.