Yes an RSS feed would be the way to do this. An RSS Feed reader is built into vBulletin. Go to the Admin CP -> RSS Feeds -> Add a New RSS Feed
You select a username who will make the "post", you select which forum it will post to, and a bunch of other settings.
The only tricky part is the "new" twitter design hides the RSS URL, you need to switch back to "old twitter" - view the profile of the twitter user, and on the right side near the bottom will be an RSS Feed URL- that's the URL you enter into vBulletin... for example my twitter feed URL is:
Code:
http://twitter.com/statuses/user_timeline/178151128.rss