For a object to be captured by some bigger ‘planet’ and made to orbit it seems like something needs to happen. Either a collision, or other force (perhaps a co-orbiting body), needs to basically slow it down so it won’t just exit the other side. Can frame shifting accomplish this alone? Which I understanding the effect of gravity of a rotating object.
I think you mean frame dragging, not frame shifting.
In principle, yes, it’s possible, but lots of luck pulling it off with anything short of a black hole. Effectively, it’s still a three-body interaction; it’s just that the gravitational field is itself the third object.