It was a Roman custom related to various superstitions and worship of false gods. They believed the ring should go on your ring finger since the vein there goes to some particular place (the heart maybe)?
From Wikipedia:
I see zero need for Christians to continue these pagan practices.The earliest use of jewelry to signify a bonding was often chains and bracelets. This evolved to the use of the symbolic ring. In ancient Egypt, the Sun and the Moon gods were feared and worshipped. A ring was a symbol of these spirits, both of whom were also related to the home and hearth. The endless circle showed the eternal nature of the bond, while the open centre was meant to be a doorway to things unknown.
This tradition was later assimilated by the Greeks, after Alexander the Great conquered Egypt in 332 BC. Up to this time betrothal rings were generally made out of hemp, leather, bone, or ivory. In early Rome the use of metal rings gradually began to take over from these materials, and the metal of choice back then was iron. Gold and silver rings were given on rare occasions, to prove that a man trusted his wife with his valuable property.
As far as trusting the wife with valuable property - pretty much every plain Anabaptist has their house and business and vehicles with their wife’s name on the deed or title. That seems more significant to me than a wedding ring…