I'm unsure what the preocess is for determining beneficiaries of US citizenship but I it probably is certain that they also employ DNA science to determine the relationship, however, you would have to establish contact with him so he knows your intentions as well as provide what they require for the test amongst other things they may require. Perhaps others more versed in this process can provide much more accurate details.
Even if the OP's father's name had been mentioned on her birth certificate, she was still born out-of-wedlock, since at the time her father was married to somebody else and her mother was not married at all. For such cases (birth abroad out-of-wedlock to a U.S. citizen father) it may be possible to derive citizenship through the father (in which case the OP may be a U.S. citizen already, without knowing it), under the "new" Section 309(a) of INA, but the requirements there are quite complicated:
http://travel.state.gov/law/citizenship/citizenship_5199.html
In particular, proving that condition 5 was satisfied may be difficult or impossible now, depending on the particular circumstances:
"5. While the person is under the age of 18 years --
* the person is legitimated under the law of his/her residence or domicile,
* the father acknowledges paternity of the person in writing under oath, or
* the paternity of the person is established by adjudication of a competent court."
If the OP has a green card and her mother became a U.S. citizen before the OP's 18th birthday, the OP might have derived U.S. citizenship through her mother, under the provisions of the Child Citizenship Act.
If neither of these are applicable, but the OP does have a green card, she can file N-400 and apply for naturalization herself, based on being an LPR for over 5 years.
If she never received a green card, but was living in the U.S. basically out of status all this years, she may have a serious problem. Basically, a lot here depends on the particulars which OP has not provided above, e.g. the information about her and her mother's LPR status; how exactly (in which visa/immigration status) they were admitted into the U.S. in 1992, etc.