Dr Barry Morgan, who has been Archbishop since 2003, listed the Republican's election win in November among a catalogue of events which he says show we live in a "divided" world.
Appearing to reference Trump's comments on controlling migration from Mexico, the Archbishop said we need to be building bridges in 2017, "not walls".
Dr Barry said the election of Donald Trump, the Brexit vote, the migration crisis and the conflict in Syria highlight how we occupy a "brutal, bloody, divided, torn world that seems at times to be out of control and unpredictable".
He said: "In countries such as Britain and America, there is bitterness in the air, about Brexit in the one case and about a president who has come to power despite his appalling remarks about women, people of other faiths, and Mexicans.
"But the fact is that in spite of all the outrageous revelations about him, Donald Trump was still elected. What does that say about those who voted for him in a country where most people still claim to be religious?"
Encouraging people to show tolerance and grace in the face of hateful or extreme views, the Archbishop pointed to Jesus as setting an example for how they should live.
He said: "And the resurrection of this baby in a cradle who mixes with undesirables and sinners, offering the hand of friendship to those who don't deserve it, is actually God's endorsement that this is the only way to live and love because they are the values of His Kingdom and will ultimately win out.
"May God bless us as each of us tries in our small way to live that kind of life."