Our rabbis taught: Everyone may go up as one of the seven Torah readers, even a minor and even a woman. However, the Sages said that a woman should not read from the Torah, because of the dignity of the congregation (kavod hatzibur)

(7) [With regard to] all commandments about one's son which are obligatory upon the father, men are obligated, and women are exempt. And all commandments about one's parent which are obligatory upon the child, both men and women are obligated.

And [with regard to] every positive commandment that is time-dependent, men are obligated and women are exempt. And [with regard to] every positive commandment which is not time-dependent, both men and women are obligated. And [with regard to] every negative commandment, whether it is time-dependent or it is not time-dependent, both men and women are obligated [except those regarding anatomy].

(8)... This is the general rule: all those who are not obligated to carry out a particular action, cannot release [others] from their obligation.