A Full Stack Developer handles every part of the web application. If you do not do all the CSS (and HTML, I presume, because only doing CSS without HTML sounds really strange?), even though you probably could, you can still call yourself a FSWD. It really is a loose term, so don't worry too much about it! Let me quote SitePoint:
The term full-stack means developers who are comfortable working with both back-end and front-end technologies.
To be more specific, it means that the developer can work with databases, PHP, HTML, CSS, JavaScript and everything in between, also, venturing as far as converting Photoshop designs to front-end code.
A full-stack developer doesn’t need to master all of the areas and technologies he needs to work it, because that just makes it nearly impossible, he just needs to be comfortable working with those technologies, and that’s a lot too.