My father refuses to marry me off without a reasonable cause. What can be done?

If a father refuses without a valid religious reason to marry his daughter to a man of suitable standing (sekufu), this is called wali adhal, and you may apply to the Syariah Court for a wali hakim (judge as guardian).
Allah forbids guardians from preventing women from marrying partners they have agreed upon in a proper manner. The court will hear both parties; if the father's reasons are reasonable (for example the prospective husband is not of suitable standing in religion, or poses a risk), the application may be rejected. Give priority to family discussion and counselling first, because parents' blessing brings barakah. Refer to your state's enactment and The marriage wali.