No. But bbPress support XML-RPC.
Technically feasible but practical usable solution doesn’t exist.
Twitter only supports 140 characters so if we even get the functionality to parse the tweet, there wont be much space left for the content that could be entered by the user.
Eg., the tweet could be @bbpress [new-topic] Topic Title:- Post Content or @bbpress [topic-1234] Reply Content. Then we could monitor all the tweets sent to @bbpress from forums by setting up a cron job and then do the other things..
Is it possible to signup with twitter account?
Not right now.
And this version of the software is being replaced by a wordpress-plugin.
“Sign in with Twitter” option/plugin would be amazing.
