Let's say you did your best to cast on and join to knit in the round without getting a twist, but you knit the first couple of rounds and you discover there is a twist. It happens to the best of us, not to worry. You can fix it without needing to go back if you catch it in the first round or two but once you've got a long length of material, there's nothing for you to do, but take your needles out frog the project, cast on gain, and this time check maybe three times before you join to knit in the round.
If you catch it early like I have here, I can show you a quick cheat that won't make it completely invisible, but it's good enough if you don't want to have to rip back.
So, as you can see here there is a little twist in my cast on edge, and I don't want to knit any further, because the taller it gets the more obvious that twist is going to be, and I'll actually be knitting something like a Mobius strip, so what I'm going to do is I'm going to follow the twist from the right side around.
This is really easy on a tiny project like this, but if it happens to you on a big circular knitting project like a sweater you do the same thing.
So, from the right side with your fingers you get everything aligned so your cast on edge is on the inside of the circle, push the twist as you go, then as you get up to the left needle you're going to duck the left needle into the inside of the work, and back up in here which traps the twist against the cast on edge, and if you knit past that little caught twist there you really won't be able to see much more than an indentation on your cast on edge.
It feels a little different. It feels harder where the other ones feel soft, but that is such a nice alternative. That's a small price to pay for not needing to rip out.
So I will show you again. Let's go back. There's my twist right there. I'll just go in reverse of what we did. So you're knitting around, you're knitting, you're knitting, you look down, you think " Oh no, I thought I double checked, but there is indeed a twist." So, from the right side follow the twist along. Tuck my tail here. Push it around. When you get it all the way up to the left hand needle take your left hand needle, and sort of draw a circle in the air, point to the inside of your work, come back up, and now you've trapped the twist in between the last stitch, and the next stitch, and once you knit it and move on it will be fairly invisible. Especially if you've got skinny yarn. It's fairly invisible on this big fat yarn. There it is, see the little twist? Just in there. And that is how you fix a twist in circular knitting.