This plugin allows you to create nicely textured 2D polys. Simply place a few points then create / assign the shape material and you should have a good looking polygon.
The textures used are similar to what you would use if making terrain using TileMaps/TileSets
See Homepage here:
A Sample Godot Project can be found here:
SmartShape2D + Aseprite tutorial can be found here (Thanks Picster!):