You can do this with just the serial port and a USB to serial converter with something like a RPi that will emulate a modem for you.

http://podsix.org/articles/pimodem/

However that can be replaced with a plipbox (I believe he has open sourced it and you can build your own).

http://lallafa.de/blog/amiga-projects/plipbox/

You can just plug this into the back of your PC. This is a good demonstration of how it all works.

https://www.youtube.com/watch?v=egi3MiSgV1k