No, you mixed up the cause and effect. The magnetic field is inducted by the Earth rotation. Moreover the Earth rotation pole and magnetic pole does not much exactly.
The magnetic field does not affect the rotation at all. The only "major" changes in our rotation are caused by tidal drag on the body and oceans of the Earth, caused primarily by the Moon and to a lesser extent by the Sun. Even those only change the rotation by less than 2 milliseconds per century, so to a very high degree of accuracy the rate of rotation is virtually constant during a given lifetime.
There is also a slow change in the direction of our rotation, caused by the fact that the rotation of the Earth causes the Equator to bulge out by 1/3% of the radius of the Earth, compared to the distance through the Poles, and the tilt of our axis relative to the plane of our orbit allows the tidal forces of the Sun and Moon to exert a "torque" or twisting force on the bulge that cause the direction of our polar axis to rotate around the Pole of our orbit once every 26,000 years. That changes the direction of the Pole in the sky by about 1 degree per 70 years, but does not change the rotation of the Earth itself about its own Pole.
So all significant changes in our rotation are caused by the tidal forces (a side effect of gravitational forces) of the Sun and Moon, not by magnetic fields.
Manetic fields are created by convective motions in the molten outer core of the Earth, which is believed to be a mixture or iron and to a much lesser extent, other materials. Heat from the central core is the cause of these motions, which are slightly random, but due to the rotation of the Earth tend to be parallel to the rotation of the Earth or anti-parallel to it. These convective motions create a multitude of small magnetic fields, which add together in a more or less random way, but since they are mostly parallel to or anti-parallel to our axis of rotation, tend to make the overall magnetic field that we observe at the surface more or less aligned with the rotational axis. However, the sum of the individual magnetic fields in the core does not have to be exactly parallel to the overall rotation of the planet, and the way in which the individual fields add to or subtract from each other undoubtedly involves random changes over long periods of time. One result of this is that the magnetic poles wander over time (in recent years, the North Magnetic Pole has been moving nearly 50 km/year; it used to be in northern Canada, and is rapidly heading toward northern Russia); another is that every few hundred thousand years the field becomes much weaker, then 'flips' to the opposite direction, so that compasses that now point North would then point South. Such changes are thought to take place in time scales very short compared to ten thousand years, and perhaps much shorter than a thousand years. Many scientists suspect that a general weakening in the overall field and the rapid change in the position of the North Magnetic Pole may portend an imminent flip in the field, but what the field would be like during a flip is a matter of controversy.
In the preceding paragraph, I hope I made it clear that the overall field is drive by more or less random convective motions due to the heat of the core, and that the rotation of the Earth tends to organize the field so that it is more or less parallel to the axis of rotation. So the statement made in another answer that the rotation causes the field is to a certain extent true. It doesn't actually create the field, but it does influence the orientation of the field most of the time. But since the convective motions are presumably at least somewhat random, there is no reason why the field must align with the rotation at all times, and during flips, it is probably far more complex than anything we're used to.
(Final Note: I've rushed through this as I need to get up very early tomorrow, and haven't taken the time to edit it. I don't think that has significantly affected its clarity or accuracy, but apologize if it has.)
Broadly speaking, conservation of angular momentum maintains the North South Axis of rotation. Nutation and Precession are oscillations of axis of rotation, but the axis on which Earth rotates remains same. To change the axis of rotation, external torque is required. For example, Tidal forces from Sun and Moon changes the speed of rotation of Earth (tidal locking, Earth's day length has increased over time). Due to rotation of Earth, the magnetic field came to existence-dynamo effect. So Magnetic Field is the effect of Earth Rotation. Magnetic Field does not maintain N-S Axis of rotation. It may have small effect as Earth may feel Magnetic force from external source (majorly from Sun) in small magnitude, but it can not change/maintain altogether the N-S axis itself.
The axis of rotation is different from the magnetic poles. This difference creates force for the earth to rotate on its axis. The same is the case with all planets in the Solar System. Moon doesn't have Magnetic field; hence it does not rotate on its axis.