https://github.com/jakajancar/DropboxUploader

Install software: 

opkg update
opkg install php5-mod-curl
cd /www
wget https://raw.githubusercontent.com/jakajancar/DropboxUploader/master/DropboxUploader.php
nano upload.php
<?php
require 'DropboxUploader.php';
$uploader = new DropboxUploader('email@address.com', 'password');
$uploader->upload('path/to/a/file.txt');
?>

send a command  (http://ip_address/upload.php) over the internet to trigger the upload.

login dropbox to confirm file is there.