Can't find Corruption

Unfortunately, in Terraria, each world will only spawn with either the Corruption or Crimson Biomes. The wiki page on the Corruption states that only during world generation will the loading screen hint at whether or not the world will contain Corruption or Crimson. From the Wiki:

You can also tell if your world will have a crimson or a corruption because by reading the text that describes the processes in world generation, such as settling liquids, it will either say making the world bloody, indicating a crimson. If corruption, it will say making the world evil during world generation.

However, it is possible to create your own Corruption biome that would allow you to spawn the Eater of World, as long as you had the proper items, more on that here. From the Wiki:

Creating a new Corruption biome requires at least 200 corrupted blocks, such as corrupted grass, Ebonstone, Ebonsand or Purple Ice Blocks.

Once these have been placed in the world, they ought to spread normally as Corrruption, increasing the size of the biome. However, the only way to obtain these types of blocks (outside of cheating) would be to get them from a different character or by creating a new worlds until you get one with corruption in it. And at that point it's likely just to be your best option to fight the Eater of Worlds there, but what you want to do is up to you.

As the other answer says, you must get the required materials to spread Corruption (or Crimson) from corresponding worlds. To speed up the search, create new small worlds until you see that the tree picture in the world list menu looks like this:

Top tree means there's both Corruption (purple) and Hallow (yellow) in this world (which is only possible if you've defeated the Wall of Flesh or otherwise introduced Hallow into the world), middle tree means there's only Corruption (the one you're looking for), and bottom tree has only Crimson.

_{Image taken from this answer.}