Vedic Astrology lays down very strict rules for the finger on which a Gemstone can be worn.
The index finger, known as the Tarjani, is considered very inauspicious. It is the finger for expression of anger. Each of the four elements, Fire, Earth, Water and Wind/Air, are associated with each of the four fingers on our hand, (the thumb is not considered) and this in turn dictates the choice of finger for wearing a given gemstone.
The following table gives the information about the relationship between planets, gemstones and the fingers on which the same are to be worn.