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It depends. In GTA 1 and GTA London 1969 & 1961, you could play as several characters, including women. From GTA III onwards, it is impossible to play as a woman as there is no female protagonist -as of now-. Only the use of mods such as skin selectors can fix this.

Note: The myth that was talking about the ability of playing as Candy Suxxx in GTA San Andreas by loading a VC savegame is entirely fake. You can also be a girl in the GTA: SA multiplayer mode.