Texas Vehicle Code:

Sec. 545.107. Method of Giving Hand and Arm Signals.

An operator who is permitted to give a hand and arm signal shall give the signal from the left side of the vehicle as follows:

(1) to make a left turn signal, extend hand and arm horizontally;

(2) to make a right turn signal, extend hand and arm upward, except that a bicycle operator may signal from the right side of the vehicle with the hand and arm extended horizontally; and

(3) to stop or decrease speed, extend hand and arm downward.

Besides all that, it just seems so logically obvious: "I am going this ------> way, the way I am pointing." It seems it would be *natural*, and quicker, to recognize a person's intention if they are pointing somewhere they intend to go, rather than try to recall an arcane set of rules about bent elbows.