The Disbelieving Father May Not be a Guardian of His Daughter in Marriage
Question:

A young Muslim man wants to marry a Muslim girl, but her father, who is a habitual drinker, and an apostate always refuses. Is it permissable for this father to contract the marriage of his daughter?
Answer:

If she is a Muslim, then there is no objection to the young Muslim man marrying her. But her father may not be her guardian if he is a disbeliever; instead, her brother may give her in marriage, if she has a good brother, or her paternal uncle, or her paternal cousin, or her brother's son - if she has paternal Muslim relatives - then the nearest of them may give her in marriage. And if there is no one besides the disbelieving father, the Judge may give her in marriage.

Shaykh Abdul-Azeez Bin Baz
Fatawa Islamiyah, volume 5, The Book of Marriage, page 246