Iggy Azalea can't just "charge it" to Amex anymore ... 'cause the company's suing her famous ass for a FAT unpaid balance.

According to docs obtained by TMZ, American Express is dragging Iggy to court over a $300,000 statement ... which it says is $250k more than her preset limit.

Amex wants the full amount, plus its legal fees. 

We know Iggy lives large, she's a rapper after all, but if what Amex says is true ... let's hope she still has the receipt for the fine art that set her back $12k.  

We've reached out to her reps ... no word back.