The author of Psalm 121 is not noted in the Scripture text (as it is in Psalm 122). It is generally attributed to David. The term 'right hand' is a figure of speech denoting power or authority. It is derived from the fact that for the majority of people, the right hand is stronger than the left. Also, the Hebrew word translated 'hand' can also mean 'power' (yad).
For a fuller description of the term 'right hand' when applied to God, see our article titled 'Questions and Answers About the Oneness of God' on the Doctrine shelf of the Apostolic Free Library.