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

Dean’s Scholarship
Minimum Criteria: Based on academic performance

Alan and Jane Handler Endowed Scholarship
Total Worth: full-tuition
Eligibility: full-tuition
Minimum Criteria: Based on academic excellence, outstanding potential to be future leaders, and demonstrated mastery of complex challenges.

University of Rochester provides aids at an average of 51612 per student meeting 100% of students need. 100% of students with need receive financial aid at an average of 47440 need-based grant. They also provide other scholarships including FIRST Robotics Scholarship and STEP Scholarship.