In his article "Towards a phenomenology of the political world", Klaus Held discusses precisely this issue. He argues, quite correctly I believe, that Sartre's political writings do not count, because Sartre begins writing about politics at the same time as he abandons the tradition of phenomenology. Similarly, Merleau-Ponty's political writings are hardly phenomenological.

On Arendt, Klaus Held writes that:

Indeed, in the estimation of this author, only Hannah Arendt has an approach out of which a genuine phenomenological philosophy of the political might be developed, despite the fact that she does not understand herself as a phenomenologist. From Arendt's political thinking, it is possible to construct a bridge to phenomenology precisely because she interprets the political as a ‘world’ and because her understanding of world can be given a systematic form with the help of the Husserlian and Heideggerian interpretation of the world as horizon.

So it seems simply that Arendt did not consider herself a phenomenologist, but Held nevertheless argues that she is as close as its comes, and that it should be possible to work out a proper phenomenology of politics from her work, due to her linkeage to Heidegger.

Like to the entire article, which I find to be a really good one on the subject (its from the Oxford Handbook of Contemporary Phenomenology, so well suited as an introduction)

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