Catholicism believes in a personal God - a rational being who loves, creates as a voluntary act, and cares for His creation. Einstein found himself unable to believe in such a God:
"It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously."
(letter quoted in Hoffmann, Banesh: Albert Einstein Creator and Rebel. Cited in the Wikipedia article "Religious and philosophical views of Albert Einstein.)
When Einstein used the word "God" in the quote you cite, therefore, he seems to have meant something very different than what the Church means. So it would be surprising if the Church used the statement at all in any teaching.
That said, the Church certainly believes that God, in its use of the word, "does not play dice with the universe" - that is, he does not allow things to happen which are not beyond his ultimate control. The Church believes that all things occur subject to Divine Providence; they are all part of (or incorporated into) God's Divine Plan for the universe. Even physical events which seem random are part of what God wills for the universe:
God does not abandon his creatures to themselves. He not only gives them being and existence, but also, and at every moment, upholds and sustains them in being, enables them to act and brings them to their final end.
Catechism of the Catholic Church, paragraph 301
Thus, although the Church rejects what Einstein said of God, in that it rejects his understanding of God, She still teaches something similar regarding God as He is in truth.