The ring binder mechanism is metal and recyclable. 

Likewise some file types have metal “ports” which are recyclable IF you are able to remove them from the cover. However they are very difficult to remove.

Ring files are typically covered with either

  1. cardboard covered in vinyl (hard cover binders)
  2. plastic (soft cover binders)
  3. embossed cardboard

If you can remove the cardboard from the plastic cover, it can be recycled. 

Unfortunately this covering is often glued on making removal impossible.

The plastic covers are not made from a kind of plastic that can be recycled.