Can God use a man in ministry if he's not a "natural leader"? The short answer is yes, but there are some things to address about leadership first.
There’s a balance here. Decisions of leadership must be prayerfully made in the will of God (Ephesians 5:17; Psalm 143:8), but also practically with the reasoning of ones own sanctified mind (Psalm 119:73; Proverbs 2:9), and in cooperation with ones church (Acts 2:46; 5:12).
Another balance is that while I don’t think a pastor can simply railroad through any decision he wants (1 Peter 5:3), he also can’t expect that his decisions will always please everyone (Galatians 1:10). There needs to be a confidence that something is worth doing, but also a willingness to accept responsibility if it goes south. A man must carry himself in such a way that people trust his leadership (1 Timothy 4:12). And that last part is where the debate happens- can leadership be taught or is it innate?
In an article in Forbes, Erika Anderson, author of Leading So People Will Follow, discusses some of her resources on leaders collected over 30 years of observing and interviewing them. She concluded that some people are indeed born leaders, the vast majority of people exist in the middle where many leadership principles can be learned, and the last 10-15% no matter how hard they try, will never be good leaders.
Her statistics make me think of the Apostles. Peter, James, and John all seem to have some leadership tendencies, especially Peter. Some of the others like Andrew and Bartholomew seem content to be more passive.
We tend to think of born leaders as just aggressive, overzealous, and ambitious people, always whipping out their sword at the wrong time (John 18:10) or taking matters into their own hands (Luke 9:49, 54; Mark 3:17). Like John MacArthur says in Twelve Ordinary Men, “Some people don’t want to play in the band unless they can be the one on the big drum.” I think that stereotype might be partly true but only in undeveloped and uncontrolled leaders because maturity tempers leadership traits into things God can actually use. It seems that there is a fine line between born-leadership and narcicissm, and the wise learn not to go near it.
In Anderson’s article, she lists four things that help people grow as leaders, and as is often that case with secular writers, she touched on Biblical principles without knowing where they came from first. I’ll give them to you from scripture rather than from her article.
1) Be introspective (self-examine) (Galatians 6:1; Proverbs 14:8)
This is the concept of being self-aware. It’s counterintuitive because we often think that leaders must be outward focused primarily. Good leaders pay attention to details in themselves. Some people think they are good leaders when in fact they’re lazy, fearful, and undisciplined - everything else but them is the problem! What they see about themselves does not correspond to reality. They’re looking at things askew. Good leaders are keenly aware of their flaws, sins, and shortcomings and they blame no one else for those. They take extreme ownership and make no excuses. This makes them less focused on leading people, but instead on leading themselves. People can respect that, so consequently they often will then follow you. You’ve just built their confidence in you because you have a teachable spirit. You notice your own direction, and self-correct. No man needs to tell you.
2) Rule your spirit (Proverbs 16:32; 25:28; 1 Corinthians 9:25)
Simply put, learn to detach from the emotion of a thing, and report on it fairly.
Instead of stating you want things to turn out a certain way, you are simply reporting how it all happened. You step out of yourself to become the observer. You take note of all the events that occur during the day as the reporter or the journalist… When you become the observer, you are not trapped in the drama when times are bad… - Jeffers, Embracing Uncertainty
Allowing emotions to rule kills your ability to assess something accurately, rationally, and as neutrally as possible. Mighty men rule self first because it’s the nearest and most dangerous threat.
3) Seek wise counsel (Proverbs 11:15; 15:22; 20:18; 24:6)
Wise counsellors are objective, experienced people who think like God thinks, will be completely and brutally honest with you, and have your interests in mind when offering instruction. As an aside, there is a major difference between getting wise, objective counsel to make a decision and asking those who look to you for leadership what they think you should do. The former is wise, the latter makes people wonder why on earth they should follow you.
4) Listen without filters (Jeremiah 17:9; Proverbs 3:5; 28:26; James 1:14)
This is actually a subset of #1. If you are self-aware then you will realize when you are applying filters to what you see and hear. Filters are pre-conceived notions, assumptions, unreliable biases, and faulty heuristics. In other words, you must learn to red flag your own logical fallacies as soon as you begin to think about a thing. The result is a confident dogma that is also a balanced and equitable dogma. In short, it will make you intellectually honest, i.e. honest with yourself.
These things make you easy to follow and easy to respect. I think that in some way, every man can apply and use these things to some effect, even if they're not a "natural leader" type. I also believe that those who do not have the gift of leadership/administration may have more of a challenge learning this. But I don’t think that’s any reason give up. And perhaps by not giving up, you've proved something about yourself.