Hello dear friend,
This is a good explanation for the biblical and cultural origins of the practice:
"It has always been the tradition of the Church to place the wedding ring on the right hand of the couple based on biblical references. This is seen very clearly in one of the prayers in the Betrothal Service. A portion of the prayer refers to the biblical references: “For You, O Lord, have declared that a pledge is to be given and held inviolate in all things. By a ring Joseph was given might in Egypt; by a ring Daniel was exalted in Babylon; by a ring our heavenly Father showed compassion upon His prodigal son, for He said, ‘Put a ring upon his right hand, kill the fatted calf, and let us eat and rejoice.’ Your own right hand, O Lord, armed Moses in the Red Sea. By word of Your truth were the Heavens established and the earth set upon her sure foundations; and the right hands of Your servants shall be blessed by Your mighty word, and by Your uplifted arm.” As we see, it was scripturally the practice to wear rings on the right hand, the hand of authority and power completing the pledge of commitment. The power and authority comes from the right hand of God.
The practice of wearing rings on the left hand is rooted in superstition that says that there is a vein that goes from the left hand directly to the heart. This medieval superstition, like many others, was brought to America from Western Europe no doubt. Unfortunately, too many people today just follow what the majority in society do without truly understanding its meaning. Hopefully, with education and faith we will maintain the richness and meaningfulness of the Orthodox faith.” (taken from Journey to Orthodoxy)
God bless you!