A question from Edahani from a forum post:

What about creating a box for the whole thing? like the ones you showed on the screenshots, how come there's no setting for that? i felt conned! :p

That depends on your WordPress theme.
Some WordPress theme show/display/style their widgets in boxes.

But, you can style the Xhanch - My Twiiter widget by adding codes like this to your Custom CSS

{xmt_id}{
    border:1px solid #304061;
    padding:5px;
    background:#eeefea
}