Yes it is called aquaponics. I helped build one for the Biology Lab at Fisk University a few years ago.
You can only grow low
nutrient hungry plants like lettuce and some herbs.
The problem is that fish like the water pH 8.5 and plants like it at 6.0 so the only thing you can do is compromise at set the pH at around 7.0
It would also be a good idea not to use expensive fish because you might be feeding your plants expensive fish emulsion when your fish start croaking.