The Church does not address Yoga specifically. If the breathing and body positions are simply done for exercise and health then there is nothing wrong with it. If someone is engaging in non-Christian spirituality then that is a problem.
In the early Church the issue of the day was whether one could eat meat sacrificed to pagan idols. St. Paul answered by stating:
So about the eating of meat sacrificed to idols: we know that “there is no idol in the world,” and that “there is no God but one.” Now food will not bring us closer to God. We are no worse off if we do not eat, nor are we better off if we do. – 1 Cor 8
I believe St. Paul’s point is applicable here. There are no other gods other than the one God of the Trinity. There are no other gods to invoke so in Yoga we are merely doing exercises to keep physically healthy. If someone is engaging in spirituality contrary to the Catholic faith that is a separate issue that, imho, has nothing to do with what position their body is in when they do it.