I don't know if it's normal but my cat snores too.
It's not constant and it's not too loud but I have heard it several times. He doesn't have any health issues so in his case it's nothing to be concerend about.
You might want to run it past a vet in case the vet wants to take a quick look at the cats nose/throat to make sure there is no obstruction.
Perhaps the structure of the cat's face has something to do with whether it snores or not (e.g. dogs with shorter snouts tend to snore). Or, like people, perhaps too much weight can cause a cat to snore.