Not really. They have your IP, your browser fingerprint, your location and so on. Can't call "anonymous" a website that logs data which could easily be used to identify you.

Since Tor IPs are often banned as some users abuse them and try doing malicious stuff through them, Binance will most likely either ban your account or freeze your funds if you attempt hiding your IP through Tor as well. Bisq is the only safe option we currently have as a replacement for centralized exchanges.