Sure it is compatible and Biblical. Creationists have a huge blind spot about randomness based upon ignorance of the Bible.
Evolution happens via natural selection of genetic variation. Genetic variation is created via random errors in copying DNA.
It is the Bible, not science, that makes the case that God controls random events.
“Creationists have a huge blind spot about randomness based upon ignorance of the Bible.”
Not in my experience they don’t.
“Evolution happens via natural selection of genetic variation. Genetic variation is created via random errors in copying DNA.”
Yes of course, pretty much everyone understands that, I hope.
“It is the Bible, not science, that makes the case that God controls random events.”
Yes, and that is exactly where the problem of incompatibility comes in. The theory of evolution, and naturalistic science as a whole, doesn’t allow any room for God controlling random events. They can’t ascribe supernatural causes to anything, random or not. So, if you say that God controls the random mutations, then you do not believe in the standard theory of Evolution.