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

Johnson Scholars Award
Total Worth: Up to full tuition, standard room & board, books & supplies; summer stipend upon application in sophomore/junior year
Eligibility: Up to full tuition, standard room & board, books & supplies; summer stipend upon application in sophomore/junior year
Separate application needed: No

SCU Presidential at Entry Scholarship
Total Worth: Full Tuition
Eligibility: Full Tuition
Separate application needed: No

SCU Provost Scholarship
Total Worth: Half tuition
Eligibility: Half tuition
Separate application needed: No

Santa Clara University provides aids at an average of 36762 per student meeting 84% of students need. 97% of students with need receive financial aid at an average of 30051 need-based grant. They also provide other scholarships including SCU Incentive Grant and Santa Clara University Third-Child Grant.