Most auto parts stores sell a little kit to do this. I used one
several years ago and the mirror was still on when I sold the car a
couple of years later. The adhesive "looked" like super glue but I
can't say for sure if it was.
FWIW
YMMV
For email remove "_no_spam_"

Nope. Look for "rear-view mirror adhesive". I think 3M makes it.
Follow the instructions, being particularly careful to get everything
nice and clean, and then don't mount the mirror to the little button
for about 24 hours. If you stress the joint too soon, it will fail
again.

You need one of the glue 'kits' and to watch carefully which way is up
on the things.

There is a set screw and the metal plate comes out of the mirror arm.

The kit comes with a special cleaner and glue.  A magnet comes in real
handy for holding the metal bar in place while the glue is drying.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's