As far as I know, you would have to register a mobile number for your server with some wireless carrier. Then access it using your server, then have it process texts when they are received. It sounds like a lot of work, but definitely do-able:
SMS Tutorial: How to Receive SMS Messages Using a Computer/PC through a Mobile Phone or GSM/GPRS Modem? AT Commands
Other than that, I would set up an email address:
post@myserver.com and make a script that checks the email every ten minutes and uploads anything new that was sent in. Most mobile devices can send email they same way they do text messages. Good luck.