No, you need an OSX or IOS device to sign up to iCloud, but ......
I am planning on buying a new one and would like to get all the songs i previously bought onto my computer now. It is not showing me a Sign Up link anywhere for iCloud though. I would like to know if and how I can sign up for iCloud and get my purchased music on my PC.
...... iCloud does not do that, you need iTunes Match, which does and works on a PC.