I think if you're father renounced you are out of luck. But you should definitely check with him if you are unsure. Most countries require citizenship-by-descent to occur before a parent loses citizenship, if they even allow it at all. (A number countries do not allow citizenship by descent any more.) Your father must have been an American citizen at the time of your birth for you to inherit citizenship.
If your father didn't renounce - or if he renounced after you were born - you are a US citizen provided a few conditions are met. First of all, when were you born? The law changed in 1986.
Your father must have lived in the United States at some point in his life, and obviously your father did.
If you were born before November 14, 1986, he must have lived in the US for at least 10 years, and 5 of those years must have occurred after the age of 14. So if your father came up here at 20 or older, and you were born before this date, then you are a US citizen provided he didn't renounce before you were born.
If you were born after November 14, 1986, then the residence requirement is less: 5 years total, and only 2 after the age of 14.
(Note: Residence in a US territory also lets him meet this requirement.)
Finally, your father must be your biological father.
For details see http://travel.state.gov/content/travel/english/legal-considerations/us-citizenship-laws-policies/citizenship-child-born-abroad.html
It all depends when - or if - your father renounced.