Now why would you like to drive the relay to the specific voltage where it gets drawn or gets released? For normal operation, you would want to feed the relay 12V or 0V.

The normal way to do this is to connect a transistor between the negative side of the relay coil and ground. The positive pole of the relay coil gets connected to +12V. This is called open-collector (if bipolar transistors) or open-drain (if FET transistors) and allows the transistor to control devices with higher voltages than the 3.3V or 5V or whatever your processor may operate on.

When the transistor blocks, there will be (almost) 0V over the relay since both poles of the coil will be close to 12V, so no relay current and the relay will not be drawn.
When the transistor conducts, there will be (almost) 12V over the relay coil and the relay will be drawn.

Note that for a bipolar transistor, the transistor gain may not be enough to drive it from a processor pin, so you may have to use two transistors after each other - or buy a darlington transistor where the two transistors are integrated into the same casing. And if you use a FET transistor, you must check what voltages the FET requires on the gate to be fully conducting or fully blocked.

Note that when the transistor stops to conduct, the relay coil will try to continue to drive the same current. You should protect the transistor from this by using a freewheel diode - a diode connected over the relay coil so it shorts the coil for reverse polarity.

There are also special open-collector buffer chips that are designed for this type of problems, and that have a digital input to control if the transistor should short or not. But the buffer chips normally also requires that you have an external freewheel diode whenever you drive an inductive load.

If you try and google - or most probably also by looking at the FAQ on this forum - you will find a large number of designs where relays are controlled by a microprocessor. You'll notice that the designs looks almost identical even when the processor family or model varies.