If you did want to use Google Analytics, then I would recommend looking into PHP-GA - a PHP based Google Analytics library. So you would link to a PHP script, which logs the view in Google Analytics and then sends the file to the browser. This means that it will log every download, regardless of direct or from clicking on the link.
Here is a basic example off the Google Code page.
use UnitedPrototype\GoogleAnalytics;
// Initilize GA Tracker
$tracker = new GoogleAnalytics\Tracker('UA-12345678-9', 'example.com');
// Assemble Visitor information
// (could also get unserialized from database)
$visitor = new GoogleAnalytics\Visitor();
$visitor->setIpAddress($_SERVER['REMOTE_ADDR']);
$visitor->setUserAgent($_SERVER['HTTP_USER_AGENT']);
$visitor->setScreenResolution('1024x768');
// Assemble Session information
// (could also get unserialized from PHP session)
$session = new GoogleAnalytics\Session();
// Assemble Page information
$page = new GoogleAnalytics\Page('/page.html');
$page->setTitle('My Page');
// Track page view
$tracker->trackPageview($page, $session, $visitor);
Combine this with code to send the file to the browser via PHP, like so:
$file = 'file.js';
header('Content-disposition: attachment; filename='.$file);
header('Content-type: text/plain');
header('Expires: 0');
header('Cache-Control: must-revalidate');
header('Pragma: public');
header('Content-Length: ' . filesize($file));
ob_clean();
flush();
readfile($file);
exit;
