You have to tell what's the purpose of that button, if just an image then <img src="../twitter.png" />.
Your theme seems to be SnowFlat, and your position seems to be near the account login button.
So, you can edit your theme (supposedly qa-theme/SnowFlat/qa-theme.php) and find " public function nav_user_search()"
Put the img code somewhere below, like this.
$this->output('<img src="../twitter-icon.png" />');
If you just want another top menu item, then forget all the above, log in as admin and switch to "Pages" tab (/admin/pages), then add a new page. The hardest thing is to put the twitter image as background of that link. You can right click on the link and find the CSS class of that link, then edit with "background-img" element.