Is man's ability to reason properly a gift by the Holy Spirit?

The Bible certainly says things like your statement. There are the verses quoted in the comments. Closest to your wording that I can think of is:

1 Cor 12: "1 Now about the gifts of the Spirit ... 4 There are different kinds of gifts, but the same Spirit distributes them. ... 8 To one there is given through the Spirit a message of wisdom, to another a message of knowledge by means of the same Spirit ..."

I might also mention:

Isaiah 1:18 “Come now, and let us reason together,” Says the LORD

The Westminster Confession of Faith says, (IV.2) "After God had made all other creatures, he created man, male and female, with reasonable and immortal souls, endued with knowledge ..." That is, God created humans to have reason and knowledge. Not exactly what you said but pretty close, I think.

The Southern Baptist Convention's Statement of Faith says (section XII), "Christianity is the faith of enlightenment and intelligence. In Jesus Christ abide all the treasures of wisdom and knowledge. All sound learning is, therefore, a part of our Christian heritage. The new birth opens all human faculties and creates a thirst for knowledge. Moreover, the cause of education in the Kingdom of Christ is co-ordinate with the causes of missions and general benevolence, and should receive along with these the liberal support of the churches." It doesn't specifically say that the ability to reason is a gift of God, but it does say that Christians's should use their reason and is generally consistent with the idea of reason coming from God.

I made a brief search of the statements of faith of few other denominations that came to mind and didn't see anything specific on this. Of course the fact that a church doesn't mention something in their statement of faith doesn't mean they don't believe it -- I'm sure there are lots of things any given church believes that don't make it into the SOF.

Most every church recognizes that every good thing is a gift of God, including our reason, but I do not think any denomination assigns the ability to properly reason as a unique ‘gift of the Holy Spirit.  However to reason properly about Christ by faith many churches think can't be done without the enablement of the Spirit. assume by ‘properly’ you mean those There are gifts of the Spirit that are given to the church that make use of proper reason such as the gift of ‘wisdom’ and ‘knowledge’ (1 Cor. 12:8).  The main idea behind these gifts is that 'different' people have been given different ones.  Since all men have reason and by faith can reason properly, it can’t be then a special gift. Pure ability to reason is logically is a natural gift and it is likely, among those without faith, that none excels as high as the Devil, for his powers of reason and knowledge of the external form of religion no man could pretend.  

 So gifts like Teaching, or having wisdom and knowledge naturally relate to our reason and one who has an ‘unusual ability’ by the working of the Spirit, might have a kind of unusual ability to reason about Christ, displaying unusual knowledge or wisdom concerning him and his work.  But as already mentioned these are not recognized as a ‘gift of the Spirit' by any denomination as far as I know.  A person may be said to have his reason ‘on fire’ and under an ‘anointing’ yet this is not with respect to his ability to reason directly.

In fact, what has often marked out spiritual gift is that despite the natural weaknesses of certain men, even without strong powers of reason, people animated by the Holy Spirit have been able to convincingly present the claims of the gospel with extraordinary gifts. In the case of the Apostles who were ‘fisherman’ and who subsequently turned the world over with the gospel, the power of God at work in those real 'unnatural gifts' that he gave them, was seen, in contrast to their power of reason, or natural learning.

I think these and other reasons has kept any church from attributing reason to a gift of the Spirit, just as good-looks, strength and wealth are also not proper gifts.

Unfortunately, this really comes down to semantics. The answer depends on what we mean by the terms we're using. I'll attempt to clarify...

Pretty much every Christian would concede that every thing, including our brain, comes from God (though it may be damaged by sin). Furthermore, it is generally accepted that the Spirit is the Agent by which God brought every thing into existence. So every thing we have - including your brain, and any ability you have to think rationally - came "by the Spirit" in that sense.

But when we talk about "spiritual" gifts, or gifts "by the Holy Spirit", we are generally using this terminology to distinguish between the natural (physical) "gifts" (such as trees and brains) and those supernatural gifts that are bestowed via divine intervention after (or during) "baptism" in the Holy Spirit. (Whether you take that to be at conversion or as a separate event.) In other words, to say "trees are a spiritual gift" would be nonsensical, since we don't mean "physical gifts that were part of Creation" when we say "spiritual gifts".

Now, it shouldn't be hard to see that the ability to think rationally is not universal, so I won't put too much effort into proving that. Point being, our brains are "broken", regardless of what you take the "cause" of that brokenness to be (whether "genetic entropy", or "demonic destruction", or "divine blindness", etc.)

So, the only way "man's ability to reason properly" could be considered "a gift by the Holy Spirit" (according to the common definitions) is if there was some supernatural influence which enabled their broken mind to start working again. So in this sense...

• Yes, there are many denominations that believe God can open your eyes, heal your mind, cast demons out of you which influence your mind, provide you with wisdom (a sort of not-so-common "common sense") that you didn't already have, etc.

But If I understand your question, "man's ability to reason properly" (by the common definitions) is a term used primarily to refer to natural ability, apart from miraculous, supernatural influence (other than, perhaps, Creation). So in that sense...

• No, "man's ability to reason properly", which is a term generally used to refer to a natural ability, would not be considered a "gift by the Holy Spirit", which is a term generally used to refer to supernatural post-Creation influences.