For the purposes of magical armour, your DM will need to decide what option to use from the description in the Dungeon Masters Guide. This could involve armour that "magically adjusts" which is great for Wild Shape since Beasts come in all shapes and sizes.
In most cases, a magic item that's meant to be worn can fit a creature regardless of its size or build. Many magic garments are made to be easily adjustable, or they magically adjust themselves to the wearer. (DMG, p.140)
However, from the intention of your question I gather that you want to increase your AC while shape-shifted into an animal shapes. The AC for most beasts is 10-13 at best, which is not great. There is an alternative solution though if you are allowed to multiclass in your campaign. You will need to have a minimum score of 13 on your Dexterity and Wisdom (PHB, p.163) to access this option, but it will be well worth it. You can take 1 level as a Monk! This gives you Unarmored Defense (PHB, p.78).
Unarmored Defense: Beginning at 1st level, while you are wearing no armor and not wielding a shield, your AC equals 10 + your Dexterity modifier + your Wisdom modifier
This feature can be awesome: so long as you don't wear armour or wield a shield you get an AC bonus. For this to be effective you will need to try to get your Dex and Wis scores as high as possible. Your Wisdom score is the nuts-and-bolts of your Druid casting, so that's probably not a problem; just make sure you have a good Dexterity score, too.
If you start off with 15 in both Dex/Wis, you will get AC 14 (10+2+2) right from the outset (including in your Wild Shape); by level 4 you get the option to add +1 to both Dex/Wis which will mean that you get AC 16 (10+3+3). This is just as good as Barkskin and requires no concentration and is always be active. It also means that you can cast other concentration spells and then Wild Shape. Bonus!
Now, going back to the magical armour question. You might still be able to use an AC enhancing magical item in Wild Shape which is neither armour nor a shield and still benefit from the Monk's Unarmored Defense feature. Get hold of a Ring of Protection! You will gain a +1 bonus to AC and saving throws while wearing this ring (DMG, p. 191).
In response to the comment. I am not able to find a specific entry on rings, however this entry would suggest that wearing a Ring of Protection would be fine for a wild-shaped Druid:
Can a familiar attune and wear or use a magic item?
There will need to be a bit of discussion at times with the DM, as to the practicality/wearability of it. However, it is important too, to remember that even within the playable races of D&D there is great variance. The ring that would "realistically" fit a Kobold would be very different from that of a Loxodon. Yet, if one found it as loot, it would be a very mean DM who did not allow a Loxodon to wear the Kobold's magical item, and vice versa.
In our current campaign, our DM allowed our druid to incorporate a Ring of Water Walking into its ear while whild-shaped into a War Horse - sort of like a piercing. Other options would be a toe-ring or nose-ring or tail-ring.