I drag a rotated object to a parent - and it has totally different rotation.

When I make a scene in Unity I try to drag some objects to the parent object and if some of them were rotated - when dragged they have wrong rotation, everything look very bad.

How can I fix it?

I’m guessing you are doing this in 2D, and you are dragging a non-empty game object onto another non-empty game object, since I have replicated your issue.

Create an empty game object (GameObject → Create Empty) and drag all of your children objects onto the empty game object: this will keep their individual rotations.