According to Wikipedia, the writing was (mostly?) by Brian Reynolds [1]. There's an interview [2] which is linked to by the Wikipedia page about the game [3].

[1]: https://en.wikipedia.org/wiki/Brian_Reynolds_(game_designer)

[2]: https://web.archive.org/web/20050221102608/http://pc.ign.com...

[3]: https://en.wikipedia.org/wiki/Sid_Meier%27s_Alpha_Centauri#I...