Well, we'd need to apply 40 km/s of delta-v. The moon weighs 1/80th as much as the Earth. By the rocket equation, we'd have to throw the material of the Moon away from Earth at 3219 km/s or 1/100 of the speed of light in order to accelerate Earth enough.

We'd have to figure out how to get the earth spinning beyond the escape velocity of the Sun. So, probably not just by manipulating the orbit of the moon.