Yes, caver is in the scrabble dictionary.

Is there such a word as caver?

a person who studies or explores caves.

What is the difference between a caver and a Spelunker?

A spelunker enters a cave for recreational, touristic purposes while a caver explores the cave for professional, geological reasons. So if you are wondering about the difference between caving vs spelunking, one is recreational and the other is usually for scientific purposes.