At issue is whether the university's policy of seeking to enroll more black and Latino students discriminated against a white student who was turned down for admission.
Two years ago, the justices debated the Texas case for most of their term, but failed to issue a clear ruling. Instead, they sent the case back to a lower court to reconsider the university's policy, but it was upheld again.
The court announced Monday it will hear the white student's appeal in Fisher vs. University of Texas.
The case, to be heard in the fall, could pose a threat to the college and university policies across the nation that include admission preferences for qualified minority students.
Lawyers for Abigail Fisher, the white student who was turned down at the Austin campus, argued the Constitution's guarantee of equal protection of the laws forbids any use of race as a factor in admissions. The young woman enrolled instead at Louisiana State University and has since graduated.
Nonetheless, her lawsuit against the University of Texas remains alive. Justice Elena Kagan said she will sit out the case, leaving at least a possibility the justices could split 4-4 and fail to issue a ruling.
On Twitter: @DavidGSavage