One thing I'd suggest is to take some time to read some of the discussions on this website, particularly those that take place in the comments below answers. There are quite a few 'characters' on here (I mean that affectionately), and it could help give you an idea of what anarchists are like in an informal setting, just talking to each other.
One other thing, be careful that your character's anarchism has a purpose, so that it isn't just a curiosity, doing little other than attempting to embody an exotic ideology, devoid of any actual character/personhood.
Best of luck, and hope you'll stick around :)