Hello Kolistus,
Forgive me if I am repeating here, as someone else may have already give this answer.
First of all, the 'right hand' is mentioned only in Rev.13:16, in other places such as Rev.14:9, it just states the hand. However, my answer may be that, the right hand with God is the place of favor/honor. A few examples of this being, Jesus ascending the 'right hand' of the Father (Mark 16:19), the judgment of the sheep and the goats, with the sheep being on the Lord's 'right hand' and the goats on the left (Matt.25:33), the seven stars which represent the seven churches being in Christ's 'right hand' (Rev.2:1), etc. That said, I believe that the reason for the mark going into the right hand, is Satan's way of mocking God, because those who receive the mark will be worshiping the beast and not God.