In one of our recent Projects, we were faced with a requirement to scan incoming files for virus. The problem in the project was that the files after begin uploaded, were made public available on the website.
The way we solved the problem was to implementing https://www.virustotal.com/. Its a free online virus scanner that has a public API. You can send files via SSL.
We implemented the solution by adding newly uploaded files to a Sitecore workflow. The workflow would handle the scanning of files, and move the files to the final stage of the workflow, if the files wasn't infected. If a file was infected, the file would be deleted.
A Scheduler is running every 5 minutes to check for new incoming files with the workflow.
This also means that the files aren't available straight away, as the scheduler has to check the file, but you should be able to implement the functionality directly when the user has uploaded the file, by adding your custom code to the upload pipeline.