In 2023, this question is still one of the most prominent search engine results when typing "DirectX C#". Therefore, here is a renovated answer:
Since 2013, the answers to that question have been coming and going.
Here is a little guided tour:
1. Wrapper libraries
DirectX is designed to be programmed in C++, so for a decade some people have attempted to write interop libraries and wrappers to use it in C#.
You can find several of those libraries with search engines, the most recent being mostly targeted at Visual Studio 2017 and DirectX11.
Some examples :
The problem is that those were mostly projects working "around" DirectX's official development effort, the support can be limited. SharpDX was very promising but the support stopped in 2019.
2. Mono
For some time, Microsoft has pushed Mono to make games. That's not exactly directX (I didn't research it but I bet it does rely on it, though) however it's definitely made for cross-platform, high-performance (accelerated) graphical applications. In a way, you could say that it is "better" than DirectX.
the problem is that Mono has stalled and in 2023 is no longer bleeding edge.
3. Unity
Unity lets you work directly in C#. And lets you make fully-fledged high-performance, interactive graphical applications. Just like Mono, it's an advanced engine on top of DirectX. And an IDE on top of the engine.
I guess that Unity's very existence it's telling you that the industry is moving away from accessing DirectX "directly" (unless you can program in C++, obviously) and instead use a "real" environment. Game development has become so complex that there's no in-between offer anymore.
3bis. Unreal Engine?
I don't know if there are C# wrappers around Unreal Engine but I wouldn't be surprised. Just like Unity it's much, much more than "just" DirectX so it's up to you to decide if it's "too much" depending on your needs.
4. ComputeSharp
But do not despair!
ComputeSharp is a production-ready C# library meant to use the GPU mostly for computing. It's modern, well-maintained, well documented.
It's designed for computing BUT their Sample applications show you how to interop with WinUI, UWP and others (so that you can draw pixels onto the screen). Plus, it lets you access any underlying DirectX resource that you might need thanks to special binders -- those require a tiny bit of effort because you need to switch your brain to "C++ mode" even if you're still in C#. Just go along with it. Read the documentation, you should be fine.
So in some places it resembles C++ very much (again: even in your C# code) but you can still fully benefit from C# -- especially in the shaders, which is awesome.
CONCLUSION
I don't know exactly what was the intent of the original poster's question.
Butin 2023 if YOUR goal is to use the GPU, draw pixels onto the screen and write a "regular" graphical application on Windows (with sound, input/output, etc.) without relying on the absolute monster that is Unity, then I'd go for ComputeSharp.