It is not permissible for a woman to be appointed as a judge
Question

                Is it permissible for a woman to be appointed as a judge (qaadi) in Islamic sharee’ah?.
Praise be to Allah.Shaykh Ibn Jibreen was asked whether it is 
    permissible for a woman to be a qaadi. He replied: 
It is not permissible for a woman to be 
    appointed to public positions which generally require speaking with men, mixing with them and going out frequently, asking questions of non-mahram 
    men, and answering their questions. Such behaviour indicates that a woman is careless and audacious, which will lead to her giving up her modesty. 
    This position also requires her  to raise her voice. That is contrary to her femininity and modesty. Similarly a woman cannot become an imam or 
    khateeb or lawyer who has to frequent the courts and offices which are filled with men. 
This is also a kind of imitating men, and the 
    Prophet  (peace and blessings of Allaah be upon him) cursed women who imitate men. 
With regard to jobs which a woman may need, 
    there is nothing wrong with a woman being appointed to them, such as teaching female students, being a doctor or nurse treating female patients. A 
    woman may also work in offices that are visited only by women, so that women will not be forced to mix with men, which may be a cause of spreading 
    wanton display (tabarruj) and unveiling, and other things that lead to evil and immorality. And Allaah knows best. 
Al-Lu’lu’ al-Makeen min Fataawa al-Shaykh 
    Ibn Jibreen, p. 304. 
For more information on the evidence, please 
    see question no. 20677.