The word comes from the root 'ras' which in this context means taste, pleasure. 'Rasik' and 'rasiya' are two words made on the root which have the same meaning.
Rang rasiya is more or less the same as rasiya. Literally it would translate to a pleasure seeker from color, or from colorful things, but more or less the meaning remains the same. Oxford dictionary says 'rang rasiya' would mean a voluptuous or lascivious person, which basically means it's a person who is interested in sensual pleasures.
The word 'rang' in rang rasiya also gets important in context of the film Rang Rasiya, as the film is based on the life of Raja Ravi Varma who was a painter, and 'rang' literally means 'color.'