[Salik Syed]

No, it is probably not going to be feasible to apply a "small amount of current" to keep it from moving.
Different angles of the arm result in a different amount of force being applied in the downward directions. Thus one amount of current may hold it in place, but at a different position it would do nothing or even cause the arm to move.

The only feasible solution is monitoring arm position via a Pot (recommended!)

or using a locking worm gear transmission ( this will work but I wouldn't implement a worm gear simply due to the fact that it locks... maybe if you need a massive reduction with small amount of space