Get a Dragon Mask
Each of the dragon masks from Hoard of the Dragon Queen lets you add your Charisma modifier to your AC as long as you aren't wearing armor.
Draconic Majesty. While you are wearing no armor, you can add your Charisma bonus to your Armor Class.
Unearth an Oath of Heroism
The Unearthed Arcana paladin Oath of Heroism can temporarily add a bonus equal to their Charisma modifier to their AC using Glorious Defense:
When a creature you can see hits you with an attack roll, you can use your reaction to gain a bonus to AC against that attack, potentially causing it to miss you. The bonus equals your Charisma modifier (minimum of +1).
Become a Swashbuckler (NPC)
But not the normal kind. While the rogue archetype by the same name does not grant such a feature, the Swashbuckler NPC has a trait adding it's Charisma modifier to its AC:
Suave Defense. While the swashbuckler is wearing light or no armor and wielding no shield, its AC includes its Charisma modifier.
However as it is a humanoid monster/NPC, the only way to get the trait is through shapechange or true polymorph, and there are probably better things to do with your 9th-level spells.