While there might be a way (WebDAV is hint), think you need to consider some things ...
First, where is your server? Hosted remotely or on a local server to your internal network?
Where is your PC? At home ... or a workstation in your classroom/office?
Think your network/firewall people might have some concerns over that sort of setup.
Many, many, many moons ago had a PC in a computer lab at 'the office' and desired to access a directory on that PC from a web facing app on a true internet server. While very insecure the set up was also very unreliable. The PC had to be on all the time. Because it wasn't a server yet needed to have fixes and patches just like everything else did had it set to auto-update and from to time, some interaction required on reboot. Or an electrical brown out rebooted the box and for some reason it got hung on reboot.
For others reading ... yep, dumb I know .... but it was 1994 or so.
What happens if your PC's antivirus didn't pick up on a malicious file and students 'discover' it via link provided by your Moodle etc., etc. Since it was a file from your infected PC, shouldn't you be the one that cleans up the students machine?
You (*and your students) might be best off all the way around using things like Google Drive, DropBox, etc.
2 cent opinion of course.
'spirit of sharing', Ken