Does class rank matter when applying to a college, specifically Rice University?

Generally speaking, most schools aren't going to turn you away because of something like class rank. They're going to look at your application as a whole and judge based off of that. Your school will also send them a "profile" about your school which Rice would use in conjunction with your application. You currently are in the top 12% of your class so even if they did consider class rank highly I would imagine being in the top 12% with a 3.9 GPA isn't going to get you turned away automatically. In addition, this is from their website on admissions:

"Rice selects a group of applicants who, considered individually and collectively, will take fullest advantage of what we have to offer, contribute most to the educational process at Rice, and be most successful in their chosen fields and in society in general. Our evaluation process employs many different means to identify these qualities in applicants. History shows that no single gauge can adequately predict a student’s preparedness for a successful career at Rice. For example, we are cautious in the use of standardized test scores to assess student preparedness and potential. An applicant is considered in competition with all other applicants. In making a decision to admit or award financial aid, we are careful not to ascribe too much value to any single metric, such as rank in class, grade point average, or standardized test scores."

They have more information on what they look for in admitting students but I didn't want to make this answer a mini essay. I definitely recommend taking a peek at this link: https://ga.rice.edu/undergraduate-students/academic-policies-procedures/admission/ which should hopefully reduce some of your worries.

Good luck with your applications!