Haley, 51, dug into the difference in ages between 80-year-old President Joe Biden and her challenger Trump, who's 76.
She enters the race trailing Trump and other would-be challengers in public polls.
A Morning Consult poll on Tuesday, for instance, shows Trump backed by 47% of Republican primary voters, while just 3% of respondents said they would pick Haley.
Haley's widely anticipated announcement makes her just the second candidate in what's likely to become a wide Republican primary field.
"Haley's entrance officially kicks off a messy 2024 primary race for the MAGA base that has long been brewing," it said.