Is there any way to control current precisely with Arduino without using a DC-DC converter?
The Arduino (like other microcontrollers) is a digital device. It doesn't "control current" on its own. It has outputs which can either be off or on. Off is 0V and on is 5V (assuming you are powering it from a 5V supply). The continuous current you can drawn from output pins is 20 mA.

You can use PWM to effectively reduce the power output (for example, a 50% duty cycle would be half on and half off, thus you would have 50% power).

If you drive your torquer from some sort of transistor (eg. a MOSFET) then PWM could conceivably achieve what you are wanting to do. A link to this device would be helpful. Plus, the other circuitry you have in mind.