I will begin by presenting de Sitter's historic computation of the geodetic spin precession. Then, I will consider the toy problem of a gyroscope orbiting a non-spinning black hole where the gyroscope's mass will act as a perturbation on the background Schwarzschild spacetime. I will introduce the gravitational self-force due to this mass and look at its conservative effect on the spin of the gyroscope. I will show how to translate this effect into a coordinate invariant, in-principle-observable quantity corresponding to a precession angle for the gyro spin axis. I will show numerical results for the self-force correction to the gyro precession for both circular and eccentric orbits. I will complement the numerical work with analytically derived second-order post-Newtonian expressions.