The high court did not decide the constitutionality of UT's admissions policies, but instead sent the matter back to the Fifth Circuit Court of Appeals.
The ruling was made in the case of Abigail Fisher. She sued UT after she was denied admission in 2008.
UT President Bill Powers defends the use of race is some admissions as a way to achieve diversity. He says the school is following admissions standards upheld by the Supreme Court 10 years ago and he's encouraged by the new ruling.
"It leaves intact the Bakke-Grutter framework that narrowly-tailored use of ethnicity is constitutionally permissible for institutions of higher education."
In issuing its latest ruling, Supreme Court justices said the Fifth Circuit didn't apply the highest level of judicial scrutiny when it upheld UT's plan.
The school grants most admissions based on high school class ranking, but race is used as one of the factors in admitting about a quarter of its incoming freshmen.