We know that for a moving-coil galvanometer, the relation between current, i and deflection, θ can be expressed as,

Where k is the torsional constant, A is the area of the coil, n is the number of turns and B is the strength of Magnetic field.

From the above expression, we can see that the current is directly proportional to the deflection. And hence, if the current is doubled, the deflection will also get doubled.