I do not know what the law allows, but in principle a government could give such power to its central bank, and there is some precedent (the ancient Romans had a system of private tax collectors, who would basically pay the government for a kind of license to collect taxes). I am not sure there would be much of a point, since the Fed can always raise interest rates, which has the same effect on the supply of money and ultimately affects the general population in the same way (you are left with less money to save/invest/blow on parties). Taxation is somewhat more direct e.g. higher property taxes have to be paid immediately whereas a fixed rate mortgage will not suddenly become more expensive when interest rates rise, but in terms of stabilizing the value of money it does not make much of a difference one way or the other. The fact that taxes are more direct actually makes taxation the preferred tool of politicians, who typically resort to tax cuts when they are desperate for votes or propose taxes on the wealthy in order to rally support from the working class.