This is for the television series, because that is what started it all. Actually wait, no, a book started it all.
And actually, for the films (for the first at least), the theme song is just a grander, re-worked version of the television theme.
The song in question is simply referred to as “Sex And The City Theme” and was composed by American composer Douglas J. Cuomo. It was originally recorded by Mark Berman on keyboards.
However, in the original and official soundtrack—the franchise has released a lot—the theme song is a version by Groove Armada, an electronic music duo from England. I do not know if the exact same one used in the show is available commercially.
In the soundtrack of the first film, a version by The Pfeifer Broz. Orchestra is included.
Like I said, there are a lot of music releases out there for this franchise. I have found six already—at least two for the series, and a separate soundtrack and film score for each of the two films. However, the two songs mentioned above are the only commercial releases and versions of the theme song that I know of.
Below is the original intro and opening credits for the series.
Below is a music only video of Groove Armada’s take on the theme, as included in the series’ official soundtrack (volume 1).
And finally, below is the one for the first film. The one included in the first film’s soundtrack by The Pfeifer Broz. Orchestra.