I don’t think so, certainly not on a Thomistic or other classical theist conception of God. For suppose there are “brute facts.” Either they would be facts about God or they would be facts about something other than God. But surely no facts of the latter sort could be “brute facts” if theism is true. For if some fact about something other than God was a brute fact, that would entail that it had no cause, no explanation, no source of intelligibility of any sort. That would entail, among other things, that it did not have God as a cause, explanation, or source of its intelligibility. Hence it would be something which does not depend on God for its being. And that would conflict with the classical theist position that (as the First Vatican Council puts it) “the world and all things which are contained in it, both spiritual and material, were produced, according to their whole substance, out of nothing by God” (emphasis added).
But couldn’t a theist hold that while there are no brute facts concerning anything other than God, there are brute facts concerning God himself? Could he not say that God’s existence is a brute fact, or that God’s having a certain attribute is a brute fact?