It is possible to upload invoices to an SFTP server and have them picked up from there automatically. An SFTP connection provides secure file system upload over a secure channel. Tradeshift provides an account to a server where you can upload your invoices in a variety of formats.
In order to upload via SFTP, you have to activate the SFTP Uploader App in your Tradeshift account.
For a detailed documentation and guideline of SFTP connection to your Tradeshift account please follow this link: http://tradeshift.com/integrate/sftp/