Yes, it's entirely possible, but you'll have to find a tow bar first of all. They're pretty rare but do come up from time to time. Not sure if any aftermarket option exists, but there could be a solution.
I love mine - allows me to use a tow-mounted bike rack and it's simplicity itself to use. You may not have seen one because the tow head is detachable and when it's removed, there's nothing visible except a hole in the bumper but you'd have to get your head down to the ground to see it.
There is some on ebay made by GDW. The best to get is the one inclusive of 7 pin electrics. I have this one, fits and works great.
Will cost £360-00 including postage though.
Item no 252981108033.
I was led to believe early A2's can NOT have a tow bar fitted (that is, without structural reinforcements).
The Dutch "DVLA" even registers a "0" for permissable trailer weight (both braked and non-braked) on the car's registration card.
Later A2's can (I don't know when "early" ends and "later" starts) have a tow bar and are allowed up to 1,000 kg (braked trailer). They generally have the (original Audi) detachable tow head, but I have seen aftermarket "fixed head" tow bars on A2's.
The tow bar comes in handy for trips to the tip, but also for holidays: we have just finished a 5,300 km round trip to southern Spain towing a 800 kg caravan.