First of all, you have to make sure that your father satisfies the following requirement:
Child born in wedlock to one U.S. citizen parent and one non-U.S. Citizen parent between December 24, 1952 and November 13, 1986: A child born outside of the United States to one U.S. Citizen parent and one non-U.S. Citizen parent, may be entitled to citizenship providing the U.S. Citizen parent had, prior to the birth of the child, been physically present in the United States for a period of ten years, at least five years of which were after s/he reached the age of fourteen.
If you were born out of wedlock, then:
Child born out of wedlock to a U.S. Citizen father: A child born outside of the United States to an U.S. Citizen father where there is no marriage to the non-American mother is entitled to U.S. Citizenship providing the American citizen father had been physically present in the United States for the period of time as specified in previous paragraphs for children born in wedlock to one U.S. Citizen and one non-U.S. Citizen parent, either before or after November 14, 1986; and
the alien mother completes an "Affidavit to establish paternity of child" at this office before a consular officer; and
the father signs a sworn statement agreeing to provide financial support for the child until s/he reaches the age of 18 years; and the father provides a written statement acknowledging paternity.
Next, if above requirements are fulfilled, you need to apply fo US passport in the American consulate:
- DS-11 Application for U.S. Passport or Registrations (Fillable) [1001 Kb]. This form should be filled in online and printed on white A4 or letter-size paper, with each page on a separate sheet of paper
- Attach proof of your US citizenship, such as
a U.S. Birth Certificate; or
a U.S. Consular Report of Birth Abroad; or
a U.S. Certification of Birth; or
a U.S. Certificate of Citizenship; or
a U.S. Naturalization Certificate; or
a passport of your U.S. citizen parent(s) in which you are included;
Your original, long-form birth certificate: if your proof of citizenship is the U.S. passport of a parent in which you are included;
Proof of identity:
a valid passport of any country; or
a valid driver's license with photograph; or
a valid U.S. or State government ID card; or
a U.S. military ID card.
Any foreign passport that you may currently hold;
Your foreign (non U.S.) naturalization certificate: if you have acquired another nationality through naturalization or registration since the issuance of your proof of citizenship;
Name change documentation: If you have changed your name since your proof of citizenship was issued, you will be required to furnish name change documentation.
I would recommend for you to contact your local American Embassy - they will certainly help. Good luck!