Both "belief" and "intentional act" are ambiguous terms, so the answer may depend on specific meanings, even for the same author. Ordinary factual beliefs, as in Plato's "knowledge is justified true belief", are typically not considered to be freely chosen, and therefore not intentional on the common meaning of "intention" (but see the last paragraph). They function rather as constraints on intentions to act, see Belief, Intention, Intentional Action by Speaks. "Choosing to believe" is quite different from ordinarily believing, try choosing to believe that the Sun will not rise tomorrow. However, "belief" is also used equivocally for "beliefs" in values ("faith"), and often both types are mixed. Values, like hope, love, etc., or some vehicles for values, like God, karma, etc., are open to choice, and on the traditional account require intentional acts, the acts of faith. There is also perennial controversy about the nature of volition ("free will"), and hence reality of "intentions", but in practical terms the difference between libertarian and compatibilist interpretations is mostly verbal.
As examples of "spiritual beliefs" indicate, it is not always straightforward to draw the line between factual and value side of beliefs. Moreover, some factual beliefs can be subject to choice, which would make their adoption an act of will (again on the traditional account). The simplest case is the liberty of indifference, when there is no preponderance of evidence for or against a belief. One is literally free to choose, and act on it. Situations of "hoping against hope", internal conflict, when core beliefs clash with acknowledged facts, etc., show that one can even choose to believe against compelling facts. Justification of willful belief choices in the face insufficient information by necessity to act is the central theme of James's lecture The Will to Believe:
"Our passional nature not only lawfully may, but must, decide an option between propositions, whenever it is a genuine option that cannot by its nature be decided on intellectual grounds; for to say under such circumstances, "Do not decide, but leave the question open," is itself a passional decision—just like deciding yes or not—and is attended with the same risk of losing truth."
In the light of recent neuroscience experiments it has also been argued that it is the action itself that is chosen, and the accompanying belief or "intention" is a confabulation (apparently, in experiments people often time their "intention to act" to after their muscles already start contracting, if not later), see How Does Neuroscience Affect Our Conception of Volition? by Roskies.
There is also a more general meaning of "intentional act", coined by Brentano (but with roots in medieval scholastics), and turned by Husserl into a centerpiece of his philosophical phenomenology. On this view all conscious activity, "the stream of consciousness", is a flow of interpenetrating intentional acts with intentional objects, at which the consciousness is directed (in reflection intentional acts themselves may become intentional objects of other acts). On this understanding all beliefs in particular are "intentional acts" (or perhaps chains of intentional acts), for the consciousness always "intends" its objects, see Consciousness and Intentionality in Phenomenology.