Currently the only way to do this is to use the Java Weblobby: weblobby.springrts.com, which while great, still depends on Java in browsers (that has issues of its own, best discussed elsewhere) since it's meant to be used to actually initiate Spring games.
I'd ideally want to use something simple and elegant, much like the stuff that can be seen on popular irc networks: http://webchat.freenode.net/ and http://webchat.quakenet.org/. And it turns out that qwebirc is an open source project, and bibim(? he's the github owner at least) created an IRCBridge: http://springrts.com/wiki/IrcBridge.
So what I did was put qwebirc into one of my dev machines and after a bit of configuring and some changes to the source code I've made it connect to springrts. You can try it out here: http://ec2-54-213-69-69.us-west-2.compu ... onaws.com/.
Could we perhaps have it added in webchat.springrts.com, springrts.com/irc or something similar?
Example picture:
