[RPG] the AC of a Warforged Druid when Wild Shaped

The AC is the Beast's AC

Your game statistics are replaced by the statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores.

What you retain does not say "you retain your armor class" or but rather: alignment, personality, and Intelligence, Wisdom and Charisma scores. (See also the Q&A about darkvision and other physical traits)

You also retain all of your skill and saving throw proficiencies, in addition to gaining those of the creature.

That isn't AC either.

You assume the beast’s hit points and Hit Dice.

That doesn't call out retaining the druid's non-beast AC.

You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.

The standard beast - wolf, bear, giant snake, giant shark - isn't built like a warforged. It is built like a beast.

Source: Players Handbook, Druid, Wild Shape

Integrated Protection. Your body has built-in defensive layers, which can be enhanced with armor:

You gain a +1 bonus to Armor Class.

Source: Eberron, Rising from the Last War

What is true for your warforged body (race) is as true for any other race that would have their (your, to the character) elven, dwarven, halfling, or tiefling body as a druid. When you wild shape, your body is replaced by the beast's body, and the the beast's statistics replace your (the character's) usual body statistics, per the PHB description of Wild Shape, except where otherwise noted.

The description of the Warforged race includes:

Warforged are made from wood and metal, but they can feel pain and emotion. (Eberron: Rising From the Last War)

Beasts are not made from metal and wood.

Developer Commentary, if it interests you

Lead rules developer Jeremy Crawford agrees in a Sage Advice tweet:

A racial trait works with Wild Shape unless that trait requires anatomy the beast form lacks.

Rules as Fun:

If your DM thinks, as you seem to, that it would be cool for the warforged +1 AC bonus to transfer over to your wild shape, then go for it! That's a discussion you need to have with your DM as it would be a table-specific ruling.

• Balance-wise, I don't see adding +1 to a wild shaped creature's armor class as unbalancing, given that as levels go up and beast armor class is rarely that high, the beast form will still get hit plenty.

As an aside, a beast that has been magically transformed - as a warforged was created, magically - would most likely be a creature type "monstrosity" if you look at the text in the Monster Manual regarding Monstrosities, such as the Owl Bear.

Owlbear Origins. Scholars have long debated the origins of the owlbear. The most common theory is that a demented wizard created the first specimen by crossing a giant owl with a bear. However, venerable elves claim to have known these creatures for thousands of years, and some fey insist that owlbears have always existed in the Feywild.

“The only good thing about owlbears is that the wizard who created them is probably dead. ”
— Xarshel Ravenshadow, Gnome Professor of Transmutative Science at Morgrave University