Does God have free will?

God is Holy by nature. God has free will.

Free will implies choice between at least two options. If there were no options, choosing would not be necessary thus, free will would not be necessary.

God is omnipotent. There is nothing He cannot do. Including choosing contrary to His holy nature. If He cannot choose contrary to His holy nature, He would not be Omnipotent.

Faced with a choice between what is contrary to His holy nature and what is not contrary to His holy nature, He always chooses what is not contrary to His holy nature because of His holy nature.

God does not choose what is contrary to His holy nature because it is impossible for Him to do so, but rather, He does not choose what is contrary to His holy nature because He chooses to do so.

Simple.

I agree with @Software Monkey that the question's premise is flawed.

The definition in your answer is too narrow. To properly define "free will," I think we have to consider what the will is free from. Since the term, as used, is in a vacuum, we have no context, so we don't know what it is free from, without additional information.

I would suggest that a better definition would be:

The ability to choose and/or act apart from some external constraint.

If we accept this definition, then the definition you provide would be just a contextual version of this--in the context of "nature." In other words "will free from one's nature."

Likewise, we could ask the question "Do humans have free will?" and the answer may depend on context--Humans have "will free from the influence of other humans." Do humans have "will free from the influence of predestination?" I'll leave that for another question. But I hope my point is clear... The term "free will" doesn't work in a vacuum.

Now, does God have "free will?" Well, according to your definition, I would have to say no, since nothing has "will free from its own nature," apart from the possible exception of things that are able to escape this limitation by some supernatural means. And since God is the supernatural means, and there is no means greater than Him, nothing can enable Him to act apart from His nature.

I think this is like asking "Can God make a stone so large He can't move it?"

Philosophically, there is a theorem called "The Law of Non-Contradiction" that has gained wide traction in Christian Apologetics circles. (See especially Ravi Zacharias.) The "law of non-contradiction" is a simple premise - a thing cannot be both A and not A. Anything less is nonsensical.

The theological extension of this is that God cannot violate his own nature. God is incapable of lying, for example, not because he could not, but because he would not. To lie would be to vioilate his nature to do so.

Likewise, because God's will is perfect, he cannot do that which is outside his nature, because he is, by definition perfect. To act outside of what is perfect is, by definition, less than perfect. Ergo, God does not do it.

To say he "cannot" act outside of his own will is thus technically accurate, but missing the point. Whether or not he "could" is irrevelant. He simply won't.

If you want to find Biblical doctrine on this point, you might want to start at Matthew 5:48.

Be ye therefore perfect, even as your Father which is in heaven is perfect.

This comes as part of the Sermon on the Mount, at the end of a long section of commandments about choices to make in order to live righteously. After laying all of these on us, Jesus commands us to be "therefore" (related to this) perfect even as our Father in Heaven is.

From this, we can conclude that God does have free will, but, being perfect as we are told to be, He never chooses to abuse it by doing anything which would be sinful.

I would argue that the premise that free will is "the ability to act apart from one's nature" is essentially flawed. Free will is the ability to act within your power according to your nature.

However, regardless of your definition of free will, the question is also influenced by a finite viewpoint. God is both infinite and perfect. He has free will, and his will is perfect and his nature is infinite such that his will is perfectly executed. Being both infinite and perfect in nature, it is not possible for any of the three persons of the Trinity to ever act contrary to their perfect nature - that's one of the reasons it's possible for God to be three persons without inter-relational conflict.

We tend to over anthropomorphize God, and we must be very careful not to reconstruct God in our image, instead of the other way around. We image God but imperfectly; we are like him, but we are not identical to him (as if that needs to be said).

In a mysterious way, within this creation, God has created us sufficiently in his image such that we have free will; and we will according to our nature, which is fallen and corrupted. Somehow, God has organized things in this dimension (or these 4 dimensions, if you like), such that we can exercise our free will without contravening his. It's as if he has deliberately chosen to limit himself for the sake of our creation - how this resonates with his will I cannot explain... as I said, it's a mystery.