Ted Cruz' father is a Dominionist, so it seemed good to make a thread on it here. You can look up a number of articles on the false doctrine of Dominionism. I'll put links here which seem useful.
Basically, it's an outgrowth of Replacement Theology, holding that Christ will not return until believers christianize the world. In this, Dominionism comes closest to Islam, for that too is the point of Islam (which also teaches that Christ will return). Therefore all eschatology is denied or recast as the eventuality of Christians making the world ready for Christ, by converting everyone. So the Jews have no national eschatological place. For Church has replaced Israel, see.
So it's an evil doctrine, totally anti-Biblical, yielding of course all the poltical activism and uniting of Church and State that God so vehemently separated in the Mosaic Law. But Dominionists conveniently overlook the massive amounts of OT and NT verses/doctrines which prove their positions, ant-Christ.
Dave Hunt writes against Dominionism, naming those involved in it, here
. Not saying I'm a fan of Dave Hunt, I don't know his stuff well enough, but the article rings true.
Will edit this post de vez en cuando as I find more useful links. If you want to know Ted Cruz' dad's horrific teaching, just type in 'Rafael Cruz' in Youtube and pick any video where his dad (white hair, heavy Cuban accent) talks.