@orkunuslu,
I think what you're trying to say is:
Due to getting wet, I put on my coat to protect myself from the rain.
Or alternatively,
Due to the fact that I got wet, I put on my coat to protect myself from the rain.
Putting on my coat is the action I took because I got wet. I got wet because of the rain.
Hopefully that helps a bit. I'm unfamiliar with this structure.