Writing "Please Recycle" in Mandarin
I think 請回收利用/请回收利用 can apply to lots of stuff as well, for example, plastic bottles, tins, cans, glass and so on.

If you really want to be specific about recycling paper, you can try

請回收廢紙/请回收废纸 = Please recycle used/unwanted paper

or

請回收紙張/请回收纸张 = Please recycle paper

Note that the above Chinese examples are written in Traditional/Simplified.