The earth rotates, and its axis of rotation precesses due to the gravitational pull of the sun and moon and other planets upon the mass of the earth.
If an earth-sized, rotating black hole was in orbit around the sun, would its axis of rotation precess?
EDIT: I forgot that an Earth mass black hole would have a supertiny horizon. And making the horizon Earth radius means that it's heavier than the sun. So let's just scale it all up.
Consider a "solar system" in black hole equivalent: a "sun" black hole with a horizon the size of our sun, an "Earth" black hole with a horizon the size of our Earth and the same angular momentum as our Earth, and a "moon" black hole, orbiting the "Earth", with a horizon the size of our moon which is orbiting "Earth". Does the "Earth" precess? Does it experience any tidal forces?