You actually answered your own question in your op. One cup is 120 grams, or 4.23 oz.
This is about what one would consistently get if a mass of flour(typically ap) is fluffed, lightly spooned into a volume measuring cup, and leveled off with the flat side of a knife.
This is the way, pretty sure, the USDA determines flour should be measured, King Arthur Flour, etc.
The key though, in reality, when a recipe is listed with volume measures, you usually don't know how the recipe author weighted their cup of flour.
Video on how to measure flour:
Can't post the link, but KA flour has a video (youtube) on how to measure flour.