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

Presidential Scholarship
Total Worth: $14,000 to $16,000 per year
Eligibility: $14,000 to $16,000 per year
Minimum Criteria: GPA: 3.8, SAT: 1380, ACT: 29

Dean’s Scholarship
Total Worth: $10,000 to $13,000 per year
Eligibility: $10,000 to $13,000 per year
Minimum Criteria: GPA: 3.8, SAT: 1270, ACT: 26

Minaret Scholarship
Total Worth: $7,000 to $9,000 per year
Eligibility: $7,000 to $9,000 per year
Minimum Criteria: GPA: 3.33, SAT: 1190, ACT: 24

University of Tampa provides aids at an average of 16779 per student meeting 62% of students need. 100% of students with need receive financial aid at an average of 14092 need-based grant. They also provide other scholarships including Incoming Art and Design Scholarship and Army / Air Force / Navy ROTC Scholarships.