Yeah, University of Kentucky does provide scholarships based on merit. Here are some of them:

Bluegrass Spirit Scholarship
Total Worth: $8,000, with additional funding available for meritorious students
Eligibility: $8,000, with additional funding available for meritorious students
Minimum Criteria: 25 ACT or 1200 SAT and 3.00 GPA

Presidential Scholarship
Total Worth: Full Out-of-State Tuition
Eligibility: Full Out-of-State Tuition
Minimum Criteria: 31 ACT or 1420 SAT and 3.50 GPA

Otis A. Singletary Scholarship
Total Worth: Full 4-year Out-of-State Tuition plus $10,000 Housing Stipend
Eligibility: Full 4-year Out-of-State Tuition plus $10,000 Housing Stipend
Minimum Criteria: 33 ACT or 1490 SAT and 3.80 GPA

University of Kentucky provides aids at an average of 12112 per student meeting 53% of students need. 100% of students with need receive financial aid at an average of 5557 need-based grant. They also provide other scholarships including The Felix E. Martin, Jr. Scholarship and The Rogers Scholars Scholarship.