Royal blood is the same color as everyone else's blood: red. The phrase "blue blood" is a metaphor that has been used since the 1800s to refer to people of noble birth.
The term likely originated from the observation that people with fair skin, often associated with nobility who spent less time outdoors, had visible veins that appeared bluish under the surface of their skin.
The color purple has no connection to royal blood and is actually a very expensive and rare color that was historically associated with royalty because of its cost.