Robert Davidson was born in 1750 in Elkton, Maryland.  As a young man, he attended the University of Pennsylvania, graduating in 1771. During his time as a student he married a woman named Abigail, and the couple would enjoy more than thirty years together until her death in 1806.  In 1772, at the age of twenty-two, Davidson was licensed to preach by the Presbytery of New Castle and was soon sent to preach at the Second Presbyterian Church of Philadelphia. He became a professor of history at the University of Pennsylvania in 1773, during which time he worked as an assistant to the pastor Dr. John Ewing of the First Presbyterian Church of Philadelphia.  The University awarded him a doctor of divinity degree in 1784, shortly before he left the city to take up residence in Carlisle. 

Davidson came to Dickinson College as the Vice President as well as Professor of History and Belles Lettres. In 1785 he became pastor of the Presbyterian Church of Carlisle, a position that he held for twenty-eight years until his death.  In October 1785, he was named Acting Principal upon Charles Nisbet’s resignation, but in May 1786 the Board of Trustees restored Nisbet to his former office.  In 1796, Davidson was elected as moderator of the General Assembly of the Presbyterian Church.  Following Nisbet’s death in 1804, Davidson was again elected Acting Principal.  He held this position until his resignation in 1809.  He is considered the second president of Dickinson College, although he never officially held that title.

In 1807, Robert Davidson married his second wife, Margaret Montgomery of Carlisle, who was thirty-one years his junior. Unfortunately, she died in March 1809 giving birth to their second son.  Davidson resigned from his position at Dickinson College in that same year in order to devote himself completely to the church. On April 17, 1810 he married once again, this time to Jane Harris.  He continued on his duties as the pastor of the Presbyterian Church of Carlisle until his death on December 13, 1812.