This answer focuses on management not repelling, fleas have a complex life cycle, If you repel 99 of 100 fleas, that one is going to be living on you with it's family.
The internet has LOTS of yes answers to this question, random example. most are focused on animals because, well... I don't know why. People get fleas also. As rule there is a different species of flea for each type of animal they feed on (ref). But when they are hungry will snack on anything available.
There are a couple of questions on the pets.se sister site that address treatment for animals.
But when you really start to research any internet solution, (example Can dish soap really be used to kill ticks and fleas? ) you tend to find that there is more hype than fact for most claims.
The most effective solution is regular bathing and grooming. You either have fleas or not, if you are in a place that has fleas they will be on you. The most effective non-man-made-chemical-solution is to wash them away with a bath and pick or comb off any that remain. I am not sure if you want to classify soap as natural, but as the dish soap answer shows it is effective remover of fleas (not a killer of fleas).
FYI - one of the currently most popular "Natural Solutions" is 'Diatomaceous Earth (DE)' which has some health concerns. Natural does not mean without possible adverse side effects.