http://revach.net/article.php?id=4019

Section: Halacha   Category: Tshuvos
Rav Vosner - Queen Of The Jews?
The Chinuch (Mitzva 697) brings the Drasha of the Sifri that says we can only appoint a Melech and not a Malka, a King and not a Queen.  However this is not so simple.  With regard to King whose mother is born Jewish but whose father is not, the Rambam says he can be king, while Tosfos (Sotah 41 ) says he cannot become king unless both parents are born Jewish.  The Noda B'Yehuda (CM 1) says that everyone agrees that this requirement is only for the initial appointment, but if the prospective king is the son of the King then a single Jewish parent will suffice.

The Minchas Chinuch says that similarly the p'sul of a woman to be King is only if she is a new appointment.   However if her father was king, then she may rule as Queen after her father's death.  Rav Vosner in Shevet HaLevi (5:Kuntras HaMitzvos 67) disagrees.  He gives a number of reasons why a woman cannot become the King/Queen.  One reason is because she is not Chayav in all the Mitzvos like a man.  A second reason is because the King must carry a Sefer Torah with him at all times and learn from it.  Since a woman does not have a mitzva of Talmud Torah the Torah is telling us that only a man can rule.
 
Important Note: We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation.  Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.