The normal way to unlock factions is to complete a campaign (either the full imperial one or a small one)

You can also edit a text file to get acces to all factions, even those wich can't be unlocked by normal means.
In the folder:
Rome - Total War\Data\world\maps\campaign\imperial_campaign
a file called descr_strat

(when editing, it's always wise to keep a backup copy of the file you're going to edit)

Cut and paste Parthia from "unlockable" to under "playable".