Да, взгляните на dropbox-php .
Пример кода из документации:
/* Please supply your own consumer key and consumer secret */
$consumerKey = '';
$consumerSecret = '';
include 'Dropbox/autoload.php';
session_start();
$oauth = new Dropbox_OAuth_PHP($consumerKey, $consumerSecret);
// If the PHP OAuth extension is not available, you can try
// PEAR's HTTP_OAUTH instead.
// $oauth = new Dropbox_OAuth_PEAR($consumerKey, $consumerSecret);
$dropbox = new Dropbox_API($oauth);
$dropbox->putFile('newPath.txt','/local/path/tofile');