Yes...sort of.
I beleive you can only "create" a civ by editing an existing civilization. You can change the name, appearance, and attributes (such as starting technologies, civ-specific bonuses and units, etc), of any of the 16 premade civilizations.
The catch is, you can only edit civilizations by editing scenerios. Thus if you want to play a random map, you have to create such a map in the sceneario editor, (try not to look at it so that it will be a surprise) and then edit your civilization and save the scenario. Load the scenerio and you will have your random map and your editied civ(s).
I do not beleive there is any way of editing civs without editing scenarios.
To edit scenerios, simply load up "CivEdit" and then unclick the option "Default Rules" (which I beleive is under the last menu at the top of the screen, but I don't have the game in front of me). Once that is unchecked, you will be able to "Edit Rules" under one of the other menus. This allows you to edit any of the civilzations (or anything else in the game).
Hope this helps!
