No, Earth's magnetic field does not cause gravity because there are two different types of forces.

The gravity field is best considered as a static field, with the force depending only on the distance and the mass of the two objects. Although the Earth moves in the gravity field, the field itself does not.

a huge gravity field

Pluto's gravitational field strength is about 6.7% of the Earth's.

The gravitational field strength (how strong gravity is) on the Earth is 6 times stronger than on the moon.