No, there is no magnus force on the earth.
Magnus force is the force on any spinning object from the air by creating a pressure difference as the air drags with the spin.
Earth is a very huge mass with gravitational force that holds air around it. The air also spin due to gravitational effect but there is no pressure difference created by spinning earth. So, gravitational force is the only force that governs the motion of earth. And beyond small atmosphere there is empty space or vacuum so there is no magnus force at all.
There is coriolis force seen on air due to rotation of earth not drag force.
