If you want to twist a stitch you will work it through the back loops. This is fairly easy for a knit stitch, but the technique is a bit trickier for a purl stitch. It is an awkward maneuver, but it will allow you to twist a purl stitch.
1. Bring your right needle to the 'knit' side of your work away from you.
2. Put the tip into the back of the stitch from the right to the left.
3. Purl that stitch.
See it in action in this video:
