You can now include tweets in messages using the new [tweet] dBCode. There is documentation for the [tweet] dBCode in the dBCode help, but I repeat it here. You may have to do a hard reload of your browser before this will work. That's Control + Reload in Chrone, I don't know about the other browsers.
You can add tweets to your messages using the [tweet] dBCode. Every tweet on Twitter has a little down arrow in the upper right hand corner. Click on the arrow and select "Copy link to Tweet". Now paste it into your [tweet] dBCode so that it looks like this: