Canon
The Ultimate Star Wars factbook confirms that Coruscant imports its food (along with all of its other consumables) from off-planet.
Global megalopolis:
Exhausted of all natural resources, Coruscant is entirely dependent on outside support to survive
Legends
There are various mentions of hydroponic farming although with a population of trillions, you wouldn't get very far unless vast areas of the planet were given over to it.
Orbital traffic encloses the planet like electrons around a nucleus, delivering food and supplies, ambassadors and tourists.
Palaeontologists believe most of Coruscant was already paved over by the time interstellar flight became common. Such rampant overpopulation forced the inhabitants to develop the first atmosphere scrubbers, hydroponic farms, delivery pipelines, and recycling plants.