Okay, so because it IS tied to itself, that is, in theory, a circle. BUT. Now, I'll admit that I've never played a Portal game before, so I'm not sure if, in playing the games, you do get an explanation of how portals work, but I'll assume it's similar to theories of how general teleportation works. Basically, the atoms are taken apart in the original position, and at the destination, atoms of the same composition are assembled to recreate whatever's been teleported. So technically speaking, you throw a rope into the blue portal and whatever isn't still outside it doesn't exist anymore, until it comes out the orange. But it's not the SAME rope, it's just a recreation of what the rope WAS, in the place where it would now theoretically be. Therefore, you could say that the rope has been cut, then tied together again, making it a line. But because it's possible to pull on that rope, say, towards the blue portal, and it would come back out the orange, making it an infinite line.
Hell, it could probably be arugued that that IS now an infinite line, just with a knot in it every now and then, and you never actually get to the same spot once again because all you're doing is destroying old rope and forcing it to make a new rope.
Again, all of this could be wrong by the in-game science of portals, but it's interesting to think about!
That's not how portals work.(Original comment) The portals from the game are stabilized worm holes. And being that the way they work in the game and the way worm holes (theoretically)work in real life, it's both a circle and a line. Proof? Worm holes "bend" reality to link two points in space together. Causing a, sort of, tunnel from say the earth to mars. However, in the game, the warp from worm hole to worm hole is instantaneous and looks like nothing more than a hole in the wall. So by that logic it's a line.
Again, all of this could be wrong by the in-game science of portals, but it's interesting to think about!