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If I had a tiny satellite with a magnet orbiting Earth (or another body with a magnetic field), could I use this magnet to adjust my attitude?

I'm thinking it could be used in sort of the same way as one would use a reaction wheel. Just turn the magnet to where it is not aligned with the field, and wait for it to turn the whole satellite with it.

Would it be more plausible if the satellite was in geostationary orbit?

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This is called a magnetotorquer

A magnetorquer or magnetic torquer (also known as torque rod) is a satellite system for attitude control, detumbling, and stabilization built from electromagnetic coils. The magnetorquer creates a magnetic dipole that interfaces with an ambient magnetic field, usually Earth's, so that the counter-forces produced provide useful torque.

The article goes on to discuss the limitations of these devices and specifically mentions:

A broader disadvantage is the dependence on Earth's magnetic field strength, making this approach unsuitable for deep space missions, and also more suitable for low Earth orbits as opposed to higher ones like the geosynchronous.

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    $\begingroup$ The OP is asking about articulating the magnet "...used in sort of the same way as one would use a reaction wheel. Just turn the magnet to where it is not aligned with the field, and wait for it to turn the whole satellite with it." Are there articulated magnetotorquers? Maybe there are, I've always assumed they were controlled by adjusting the current in different oriented loops. I'd love to read about an articulated magnetotorquer! $\endgroup$
    – uhoh
    Commented Jan 29, 2019 at 16:58
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    $\begingroup$ If you can find one, you may be able to add another answer to Could an articulated permanent magnet work as a low-power cubesat magnetotorquer? Problems? $\endgroup$
    – uhoh
    Commented Jan 29, 2019 at 17:03

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