Strictly speaking these are two differing types of scientists.

Petrologists study rocks and paleontologists study fossils. However both these disciplines are covered in the broader training of a geologist.

Geology is the general term given to the study of the planet earth. Geology has many branches and Petrology is the branch of geology that studies the origin, composition, distribution and structure of rocks, a Geologist specialising in that area would call themselves a "Petrologist".

the study of rocks

It is called petrology.

petrologist