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

USF Academic Merit Award
Total Worth: $5,000-$22,000 per year.
Eligibility: $5,000-$22,000 per year.
Minimum Criteria: Based on academic performance
Separate application needed: No

University of San Francisco provides aids at an average of 40446 per student meeting 75% of students need. 100% of students with need receive financial aid at an average of 34598 need-based grant. They also provide other scholarships including Atheletic Scholarships and Army ROTC Scholarship.