place/d

It depends on what meaning you wish to convey.

...send me your autograph on a certain paper, which I can get framed and placed in my room.

You can get someone to frame the autograph, and then get someone to place it in your room.

...send me your autograph on a certain paper, which I can get framed and place in my room.

You are going to get the autograph framed and then you are going to place it in your room yourself.

Thanks, Contrex.