Magic tattoos all say things akin to the following:
To attune to this item, you hold the needle to your skin where you want the tattoo to appear, pressing the needle there throughout the attunement process. When the attunement is complete, the needle turns into the ink that becomes the tattoo, which appears on the skin.
They each appear on the skin, they are applied by being held to the skin. Can the metal body of a warforged use it? If so, the only other item I am aware of that has race specific requirements is the dwarven thrower.
It dawned on me that warforged aren’t considered constructs in 5e (at least I don’t think there is a distinction made for what player characters are). However, I think it should be considered that what would bar constructs from being able to use the tattoos is that the tattoos specifically say how you apply it to the skin, or how it appears on the skin. I think this would be the same disqualifying factor for warforged, or for other ‘constructs.’