The US Merchant Marine Academy also has the major:
https://www.usmma.edu/academics
but requires a nomination:
https://www.usmma.edu/admissions/application/steps-admission
Civilian colleges with naval architecture / marine engineering and Naval ROTC include University of New Orleans, the ME and NY maritime academies, and University of Michigan. Webb Institute (whose only major is naval architecture and marine engineering and where all students get a full tuition scholarship) does not have any ROTC.