She made these comments in a video dating back to "early '90s" that she submitted to the Senate Judiciary Committee last week as part of her Supreme Court nomination process.
Sotomayor admitted that her acceptance to the Ivy League schools would have been "highly questionable" if not for affirmative action.
"My test scores were not comparable to that of my colleagues at Princeton or Yale," she said on a panel for a nonprofit law organization.
In the video obtained by The New York Times, the federal appeals court judge expresses her support for affirmative action, saying that "cultural biases built into testing" make it harder for minority students to perform well enough.
Her views on affirmative action have been deemed controversial by some. Republicans have criticized her for her remarks that her personal experiences as a "wise Latina" woman will influence her judgment.
She has also been criticized for voting as a judge to back a decision by New Haven to throw out test results in which white firefighters were denied promotions because no minority applicants had scored high enough on the test.