In order to sign a message with a Bitcoin address you have to own that bitcoin address (i.e. to be yours and only yours).
Binance and the other exchanges give you an account. The address is theirs, although associated to your account. Since it's not yours, you cannot sign with it.

You can download Electrum (it would be good if you would make sure you get it from Electrum.org and also verify it), make a new wallet, make sure you keep safe the seed of that wallet, get one of the addresses and sign a message with it.