Why is my iPhone 5's home button rotating?

Chances are that the black gasket that sits behind the plastic button itself has lost it's stickiness. This is supposed to stick to the underside of the glass and hold the home button in place.

If it's not sticky anymore, I usually used a little bit of thin double sided tape at opposite corners of the round opening on the inside of the glass (this will then stick the slight plastic ledge on the home button to the screen). Reassemble and test it. If you can't get double sided tape thats thin enough, you can put normal sticky tape on the back end but it might not do much of a good job.

I would avoid using any glue as it can cause major issues and doesn't have much give to it.

Goodluck in your repair endeavors :)