Catapults are available to all factions within the game and cost 200 gold. They are effective siege weapons which can be recruited from a Siege Camp.
Note however that unlike in Stronghold 2 you do not need to place an Engineer's Guild before you can recruit Catapults from your Siege Camp.
While Catapults are primarily aimed at attacking walls, towers, gatehouses and other parts of a player's castle, they can also attack and destroy most buildings, siege camps and even units.
Note that the Ice Queen can destroy a Catapult in a single shot. Another change between Stronghold 2 and Stronghold Legends is that you do not appear to be able to fire diseased cows using Catapults anymore - from any faction.
The functionality appears to exist, but no icons ever enable allowing you to use this ability even if Dairy Farms are placed in your Castle. You can therefore only hurl rocks with your Catapults.
Catapults are relatively effective and accurate in dealing lots of damage against your intended targets, although like all weapons and ranged units, the longer the distance the less accurate they generally are. They will also struggle under lots of missile fire by ranged units, so make sure you use some Cats to protect your Catapults.
You will need 200 gold as well as 1 peasant from the campfire before you can recruit a Catapult.