I'm pretty sure the Marines don't have a height requirement (my son had a 5'2" man in his unit at one point), but they do have strict requirements for passing the physical fitness tests. There are height restrictions for certain jobs.
And you have to be a HS grad.
My son is 5' 8".5 and looks really small compared to some of the other Marines. But, he is stronger than anyone. When he was racing, he was strong and skinny. Now he is strong and buff.