As they keep saying in the news, adding another branch to the US Armed Forces takes an act of Congress. But for a military space force, the first step would probably be for the Senate to remove the US from the international space treaties, because if I'm not mistaken these prohibit such a thing. Even as polarized as Congress is at this time, I really don't see this happening.
There are some legitimate reasons for a spacefaring organization of some sort, but that should be done within the United Nations framework.
I kept wondering why none of the stories I've heard on the subject mention the treaty (treaties?). Had me thinking that maybe I'd missed some aspect that made these agreements not relevant, but I couldn't figure it out. Research time.