Can you take a picture? If it's just split, I'm not sure, but that doesn't sound like fin rot. One of my bettas is a fin nipper (nips at his own fins) and occasionally it looks as though it's split. If that's the case, it's certainly not fatal as he's about 4 years-old now.
For now, I'd just change his water, put in a little aquarium salt and some Stress Coat. But if you could get a picture, that might help.