Judith Butler is a post-structuralist feminist. See Judith Butler: her "origins" are with Maurice Merleau-Ponty and Simone de Beauvoir, Julia Kristeva, Jacques Lacan and Luce Irigaray, Jacques Derrida.
This places her squarely in the "continental" stream of thought. Specifically, that's going to put her pretty close to Derrida. Despite the phrasing, there's also not much of a difference between structuralists and post-structuralists so you could also call her a structuralist without losing too much meaning.
Even though she's from the US, there's not really any way to consider her an analytic philosopher -- either based on influences or writing style. She is most definitively not in the analytic tradition.
For more about her positions see http://plato.stanford.edu/entries/feminism-gender/
For more on the divide, how it works, and why we think she's a thoroughly continental figure.
http://philosophy.stackexchange.com/questions/21292/do-some-continental-philosophers-deliberately-obfuscate-their-writing-whyDo some continental philosophers deliberately obfuscate their writing? Why?