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

Presidential Scholarship
Total Worth: Full tuition and basic room and board
Eligibility: Full tuition and basic room and board
Minimum Criteria: SAT: 1480, ACT: 33
Requirement for maintenance: A minimum full-time enrollment and cumulative GPA of 3.25 and attendance of special events are required to maintain each scholarship.
Separate application needed: Yes
Application deadline: January 15

Vision of Excellence Scholarship
Total Worth: $29,000 per year
Eligibility: $29,000 per year
Minimum Criteria: GPA: 2.0

Capstone Scholarship
Total Worth: $24,000 per year
Eligibility: $24,000 per year
Minimum Criteria: GPA: 2.0

University of Tulsa provides aids at an average of 34596 per student meeting 88% of students need. 100% of students with need receive financial aid at an average of 8034 need-based grant. They also provide other scholarships including Alumni Grant and Sibling Grant.