Millennial GOP candidate wants to raise voting age to 25. Some young Republicans fume.

Vivek Ramaswamy, a millennial Republican running for president who would be the youngest to ever hold the job, descended on this key early state this week touting a provocative proposal to raise the minimum voting age for most Americans to 25.

“I want more civic engagement. My hypothesis is that when you attach greater value to the act, we will see more 18-to-25-year-olds actually vote than do now,” said Ramaswamy, 37, in an interview Thursday after he formally unveiled his idea at an event here. The proposal would involve meeting one of...