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

Undergraduate Merit Scholarships (Alcala, Trustee, and Presidential)
Total Worth: $18,000–$25,000
Eligibility: $18,000–$25,000
Minimum Criteria: Based upon superior academic performance including grades, course selection, and test scores.
Requirement for maintenance: minimum grade point average requirements and maintaining full-time enrollment each semester.

University of San Diego provides aids at an average of 33801 per student meeting 75% of students need. 98% of students with need receive financial aid at an average of 27519 need-based grant. They also provide other scholarships including Athletic Scholarship and Alumni Scholarships.