Les Harris

The Pressbox plugin adds a new tab to the Media Upload screen that allows you to insert images and files from Dropbox into your posts.
Additionally, the plugin provides a new shortcode that lets you add links or display images anywhere you want on your blog.
This plugin is under heavy development so please feel free to send me feedback, bug reports, and feature requests!
Credits:
This plugin bears a great debt to the work of Joe Doleson’s Wp To Twitter plugin for his excellent example of OAuth integration with WordPress.

Pressbox

Integrates DropBox with your blog allowing you to post images and files directly from your DropBox. Requires PHP 5.2 and cURL.

Jay Swadas

Add-on plugin for Contact Form 7 – adds the option to upload file directly on dropbox. 
NOTE: This plugin requires Contact Form 7 version 4.8 or later.
<h3>Usage</h3>
Simply go to your form settings, choose the “Dropbox Settings” tab and set the Dropbox access token, file input ID and dropbox folder name.

Contact Form 7 Dropbox

Thanks for this add-on solution. It helped me a lot to fulfil my requirement of file upload with Contact Form.

Easy file upload from Dropbox with Contact Form 7

A simple add-on for Contact Form 7 upload file on dropbox.

Pressbox vs Contact Form 7 Dropbox