Church Father & theologian St. Basil the Great wrote:
“No man shall let his hair grow long or tattoo himself as do the heathen, those apostles of Satan who make themselves despicable by indulging in lewd and lascivious thoughts. Do not associate with those who mark themselves with thorns and needles so that their blood flows to the earth.”
More importantly, in 787 a canon of the Second Council of Nicea banned all tattoos as a “pagan practice.” There has been no overturning of this disciplinary canon by the Church that I am aware of.
Also interestingly:
The Emperor Constantine I banned tattoos on the face in 316 AD reasoning that “man has been created in the image of God and to so defile the face is to disgrace the Divine.”