Assuming you are using a loop on the string, loosen the knots just slightly and slip the loop around to the left. Then tighten the loop knots back down. Draw to see if you rotated enough to get it to come back square. If you did, cinch it down. If not, then slip it a little more. Recheck, by draw and let down. Once you have it set — make sure the loop knots are tight enough to not slip any more.
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Start with a half twist to the right in the string below the peep. Shoot it and let it settle. If need be put another half twist in it. But if it is turning where it needs to be at full draw. I wouldn’t worry about it be slightly twisted when the string is at rest.
If the peep is in the same position when you draw back the bow then I would do as the first responder suggested. On the other hand, if the peep rotates as you draw, I would correct string rotation and then see where you are with alignment. Cinching the loop to give you a straight pull back and a straight peep is okay.
Especially if its only as much as what is shown in your pic.
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Since you didn’t mention anything about the peep rotating when the bow is drawn, the fixes are: Easiest: Slide the knots above and below the peep farther or closer apart to get it aligned. (Another advantage of the Fletcher-style peep tie-in http://fletcherarchery.com/howto_servepeep.pdf ) Most Common: Rotate the D-Loop on the string so that it pulls the peep into alignment. Best: Relax the bow and shift strands of the string to align peep.
If the peep does rotate when the bow is drawn, that is it doesn’t remain 1/8th turn to left at full draw, then the string is imbalanced. Depending on which direction the peep rotates and how much it rotates, relax bow and add or subtract twiststo lower end of string until the peep is stable. If the peep then is not square to the eye when in final position, shift strands of the string.