Perhaps quaint, but still the law (in Tennessee anyway):
2010 Tennessee Code
Title 55 - Motor and Other Vehicles
Chapter 8 - Operation of VehiclesRules of the Road
55-8-143 - Signals for turns.
55-8-143. Signals for turns.
(a) Every driver who intends to start, stop or turn, or partly turn from a direct line, shall first see that that movement can be made in safety, and whenever the operation of any other vehicle may be affected by such movement, shall give a signal required in this section, plainly visible to the driver of the other vehicle of the intention to make such movement.
(b) The signal required in this section shall be given by means of the hand and arm, or by some mechanical or electrical device approved by the department of safety, in the manner specified in this section. Whenever the signal is given by means of the hand and arm, the driver shall indicate the intention to start, stop, or turn, or partly turn, by extending the hand and arm from and beyond the left side of the vehicle, in the following manner:
(1) For left turn, or to pull to the left, the arm shall be extended in a horizontal position straight from and level with the shoulder;
(2) For right turn, or pull to the right, the arm shall be extended upward; and
(3) For slowing down or to stop, the arm shall be extended downward.
(c) These signals shall be given continuously for a distance of at least fifty feet (50¢) before stopping, turning, partly turning, or materially altering the course of the vehicle.
(d) Drivers having once given a hand, electrical or mechanical device signal, must continue the course thus indicated, unless they alter the original signal and take care that drivers of vehicles and pedestrians have seen and are aware of the change.
(e) Drivers receiving a signal from another driver shall keep their vehicles under complete control and shall be able to avoid an accident resulting from a misunderstanding of the signal.
(f) Drivers of vehicles, standing or stopped at the curb or edge before moving these vehicles, shall give signals of their intention to move into traffic, as provided in this section, before turning in the direction the vehicle shall proceed from the curb.
[Acts 1955, ch. 329, § 41; T.C.A., § 59-843.]
So there's the law and there are your feelings about what makes sense. My argument is that everyone playing by the same rules is better from the standpoint of safety. Ultimately, I don't care which arm is used to signal a right turn, but I think it's better if everyone uses the same arm.
I'm pretty sure hand signals are still taught and tested for on the written exam for a drivers license in Tennessee. What if your tail light is burned out? (I know, most people don't signal anyway.) And if a driver of an automobile is going to signal manually, they certainly aren't going to use their right arm -- in most cases in the US.
TT