This may already be known but I just discovered this for myself today and thought I'd share it. I have Widget version 1.6.2 and in the options I have 'Auto Insert' and 'Copy as Citation' checked. I logged into my Twitter account in Safari, and when I enter a verse reference in the Widget and press return it automatically puts the verse into the Twitter status box!. I also use TweetDeck and it works exactly the same way with that as well.
A very nice surprise

. Now, we just need a 'Tweet a Verse' right from Accordance itself [hint, hint ...]

-Paul