Private keys of BTC account are mainly used to sign transactions to move funds but also to sign text messages. If you are able to sign a message we provide, it means that you also control the funds in the given BTC address. Sending us a signature of a text message does not reveal or compromise your private key. Never send your private key to anyone!
You can generate a signature by using any wallet with signing capability (Bitcoind, Bitcoin-qt, Electrum, Mycelium, etc.).