Do I need to "wait" at an intersection when making a right hand turn when the light has a "RED ARROW"?

YES YOU STOP AND WAIT for the green.

The arrow only applies for the direction it is pointing.

Arrows can be to the left, the right or straight ahead.

Let the others go if they want. the ticket comes from their pocket.

Red arrow means it is illegal to proceed in the direction of the arrow.  That however will not prevent impatient @ssholes from honking at you when you are actually following the rules of the road.

Everywhere in the USA has a right turn after stopping law. That means you don't have to wait for a green light or green arrow. Just come to a complete stop and proceed to make a right turn if no other traffic is coming.

Stop it please 

Yes it does.   And even if it’s the law where you are,  to turn right on red, it’s AFTER a complete stop and AT YOUR DISCRETION .  A turn on red is not required like at a green light. It’s only for IF you are comfortable doing it.