SFTP is provided by an SSH server. So install an SSH server on your PC. Most distributions activate SFTP by default when you install the SSH server.
The machine on which you're running the server needs to be accessible from the Internet: it needs to have a public IP address, or else the site router must forward requests on a certain port to it. If you can, open or forward port 22 on the router/firewall to your machine.
If you aren't authorized to open port 22 but can open another port, make the SSH server listen on some other port. For example, if port 443 (normally HTTPS) is possible, then add the line
Port 443 to
/etc/ssh/sshd_config, wherever the configuration file is on your system) and restart the SSH server.
For what you're doing, instead of serving the file by SSH, you could serve it by HTTP. Run a trivial HTTP server that just serves files from one directory, for example
python -m SimpleHTTPServer 1234 (to be executed from the directory where you're serving the files, 1234 is the port number). If the file needs to be confidential, encrypt it with GPG. To ensure the integrity of the file, write down its SHA-1 checksum (
sha1sum /path/to/file) and verify it after downloading, or sign the file with GPG.