I know just enough CSS to be dangerous, so no warranties here. In style.css, I see:
.nav-icon {float: right;margin:13px 0 0 8px;}
I would guess you want to change the right to left - you may or may not want to play with the margins.
In the same file you find the twitter code:
#feature-footer .twitter {float: right;margin-right: 16px;display: inline;color: #777;}
#feature-footer .twitter a{color: #333;}
Again, I would change the float to left. Now, to actually move it to the top of the page, you would need to find and move that code. In includes/pro/template_feature.php,line 33, I see
<?php include (LIB . '/_twittermessages.php'); ?>
I would try moving that to header.php.
Hopefully this is not completely off base. Andrew, if I am all wet just let me know and I will be properly chastised.
Good luck.