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 permissible for this 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 beside the disbelieving father, the Judge may give her in marriage.
Source:
Shaykh `Abdul-`Azeez Bin Baz
Fatawa Islamiyah Darussalam Vol:5 no.246