I don’t know if she was actually a practicing anarchist but she had a pretty interesting take on it IMO:

My novel ‘The Dispossessed’ is about a small world full of people who call themselves Odonians. The name is taken from the founder of their society, Odo, who lived several generations before the time of the novel, and who therefore doesn’t get into the action - except implicitly, in that all the action started with her.

Odonianism is anarchism. Not the bomb-in-the-pocket stuff, which is terrorism, whatever name it tries to dignify itself with, not the social Darwinist economic ‘libertarianism’ of the far right, but anarchism as pre- figured in early Taoist thought, and expounded by Shelley and Kropotkin, Goldman and Goodman. Anarchism’s principal target is the authoritarian state (capitalist or socialist); its principal moral-practical theme is cooperation (solidarity, mutual aid). It is the most idealistic, and to me the most interesting, of all political theories.