My cousin's father was a mule and fleed the US before being detained in the 80s. Will that affect my cousin's ability to apply for a tourist visa?

Generally, everyone making a visa application to the United States is judged upon his or her own merits. A consular officer looking at an applicant for a visitor visa will usually check to see whether the individual has ties and bonds to the home country, and this may include any means of financial support. Her father would probably only come into the picture if she is dependent or even partly dependent upon him. INA 212(a)(2)(C)(ii) also makes ineligible for admission the spouse, son, or daughter of a known drug trafficker or where there is reason to believe that the person has been a drug smuggler where the applicant has within the previous five years obtained any financial or other benefit from the illicit activity of the parent, and knew or reasonably should have known that the financial or other benefit was the product of such illicit activity. That section would likely only come into effect if her father’s trafficking activities continued after the 1980s.  Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.