There is. A bunch in fact.

http://mibbit.com/

https://kiwiirc.com/

or, site-specific:

https://webchat.freenode.net/

http://chat.efnet.org/

IRC is a TCP-based protocol and browsers don't support TCP connections.

There are web-based applications that communicate with IRC but they require a proxy running on a server.

There is!

irccloud.com is pretty awesome. They have a pretty good mobile app as well (at least on android - I'm not an iOS user).

(I'm not affiliated with them, I'm just a happy user)

I use. https://github.com/thelounge/lounge (npm install -g thelounge)

I used to use: https://www.irccloud.com/ (Paid, SaaS)

Lounge is very good