Of course they do. Its name is "Congress". The Lower House of Parliament is called "House of Representatives" and the Upper House is called "Senate".
No, actually we don't have a parliament. BRTD's point is dead-on: if Congressmen in the U.S. were simply appointed by the party we would have way more women and minorities in office.
BRTD's point about party control is correct (although MP's are not simply "appointed" by their party, it's a bit more complicated than that). But that's got nothing to do with the name of the US' parliament. The British parliament is fptp too (although parties have more control on who gets nominated).
Pakistan uses first past the post too btw. And that Pakistani parliament is full of Islamists.
Yeah, I over simplified. But there's a reason why Pakistan has had a female PM, while the U.S. has not had a female president, and that reason has a lot more to do with political process than culture.
In India, Indonesia, and the Philipinnes, women have become head of state as daughters of previously prominent male heads of state or politicians, following a tradition dating back at least to Elizabeth I. Interestingly, Hillary is the front runner among women in the US by far, due to her own familial relationship. Nature has a certain way of intruding in our carefully constructed sociology.
Tansu Ciller of Turkey is the only completely self-made woman to become head of state in a muslim country, as far as I know.
Still, it is interesting that the 3 largest muslim nations in the world have had female heads of state (India has the most muslims), all less than 50 years after the birth of those nations.