Most Revd Leo Cushley used his first tweet to wish people a blessed Advent.
He picked up hundreds of followers within hours including politicians, media and other bishops.
@LeoCushley
The Archbishop took over from Cardinal Keith O'Brien in 2013 following allegations of inappropriate behaviour.
One of the first accounts he followed was Pope Francis, who has encouraged Catholic clergy to use different techniques to reach out to people.
"The Internet, in particular, offers immense possibilities for encounter and solidarity," Pope Francis said earlier this year.
"This is something truly good, a gift from God," he added.