Yup there are several exchanges that provide this currently. You can trade on Binance (up to 2 BTC), Etherdelta (unlimited), and I believe Poloniex as well (2k limit).
Binance doesn't have fiat pairs. They trade BTC / USDT which is still not fiat. Anyway they look like the only decent exchange with high unverified limits . Etherdelta is obviously working with ether and different tokens which won't be needed by OP. And before verifying Poloniex account you will have 0$ daily withdrawal limit that will extend to 25k after verification, I've been checking this thing recently. I have a few altcoin (clam, bch, btg) which I want to exchange into Bitcoin, but I don't want to give out my data.
