A circle-shaped line still wouldn't have any volume. And it could sort of get shaped by an interplay between really strong gravity and really strong centrifugal force.
That being said, I think there is some maths behind the possibility of wormholes forming from donut shaped black holes, but that's usually the sort of maths that assumes extra dimensions and interprets strange rather freely. (Which is something entirely different than the math being wrong. It just leaves us with the question whether our universe is right for the math.) The idea that you could make a wormhole this way, or in fact any way, is far more speculative than the relatively solid concept of creating a ring shaped object by spinning a mass fast enough.
Cool. That makes a lot more sense.
Still having trouble picturing actually making contract with the singularity though. Or do you skip that step and just jump through the middle like a hoop?