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In real life I'm not much for women in combat, but c'mon now, this is a roleplaying game. Sure a female can play a fighter, even in a world where female fighters may not be all that common. There are always the rare exceptions, and fantasy has a long tradition of female fighter-types. Even Lord of the Rings has Eowyn. If your DM has seen the movie, then point her or Jackson's Arwen out as examples of women can fight.
Unless your DM has some rigid reason that has to do with campaign world flavor that disallows females in the fighting profession, then you should be able to play a fighter. In the real world physiological limitations limit the number of women suitable for combat, but that is not the case in fantasy land.