If by “ring habitat” you mean a Ringworld, then the possibility is exactly zero, the same as for a Dyson sphere.
But if you mean one of these:
-well, the probability is small but above zero. That’s a Bishop Ring, a spinning habitat ~2,000km across, spinning once about every 1 hour and 47 minutes for pseudo-gravity, with walls 200km to 250km high to hold the atmosphere. The resulting surface area is around four and a half times that of Texas, slightly smaller than India. The outer shell would be woven of carbon nanotubes layered with graphene sheets.
It’s the shell that’s the big challenge: those nanotubes have to be 3,142 kilometers long and connected at the ends to make a circle, with others 1240km long woven at 45° angles plus others 1000 km long, both to reach from the top of one wall down and across the floor and up to the top of the other wall, and the graphene sheets have to be that long as well as 1000km across, and also connected at the ends so it’s a continuous cylindrical sheet. How thick you make the floor and walls depends on how you want to arrange the inside — whether you just want to fill it with rock, soil, and water and build your infrastructure on the surface, or (more sensibly) put in a hundred meters of rock and then a few levels containing subways, and service tunnels for transport, water systems, power cables, etc., filled around by more rock and topped with loose rock, dirt, and soil for the living area.
Just in case cosmic radiation is bad for nanotube cables and graphene sheets, a layer of plastic shielding can go on the outside the shell — say a meter of NASAs RFX (whatever version they have by then).
My guess is that it would require nanobots, nanometer-scale robots, to assemble those carbon nanotubes and graphene sheets atom by atom from pure carbon. That’s a lot of area, and it will take a good-sized asteroid (or three) of mostly carbon to supply the nanobots, then a bunch more asteroids to supply the metals and such for the rock layer, the buried infrastructure, the surface contouring material, and the soil, then a comet or two to get water and atmosphere. Then you’d bring chunks of selected biomes from Earth (or Mars, if it’s terraformed by then, which I doubt will be more than just really started), those chosen according to what sort of climate you want — semitropical and temperate seeming to be the best choices, with mixing depending on how you want to contour it. Having mountains lining the walls would be a decent idea, and sculpting them for recreation (from rock climbing to skiing) is kind of obvious, so you’d need some alpine forest and maybe bits of tundra along with whatever you chose for the “lower” climate.
So the big underlying question here is “Will humans have nano-scale robots that can assemble carbon nanotubes and graphene sheets atom by atom within a century?” My guess is that the answer is yes, and I’ll go out on a limb and say we’ll achieve those about seventy years from now — in which case, whether we’ll have built a Bishop ring all depends on whether it can be done in under thirty years.
A second underlying question is whether we’ll have a form of propulsion that can capture asteroids and comets and bring them to the construction location; if we achieve fusion propulsion the answer will be “yes”, and I think we will.
. . .
Note: if the assembly is done near Jupiter, some of its moons can be dismantled for the materials; this would save on fuel costs. There are twenty-two Jovian moons that are so small they don’t have names; those are the ones I’m referencing.
Since the question keeps getting asked, the light source would depend on location: close enough to the sun, mirrors would reflect sunlight; farther out an artificial sun would be needed — it’s generally assumed that we’ll be able to do that with fusion power.
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