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You cant find a giant mob in vannilla minecraft but you can sumon him using a command or a spawner.
It is not possible to actually make a mob spawner in any version of Minecraft. Mob spawners are only obtainable via in-game commands or if you use a mod of some sort.
Maybe your game level is on peaceful or you put torches around it.
If you are looking for a way to pick them up, well, you can't pick mob spawners up. You can only destroy them with a pick but it can give you a lot of exp.
Unfortunately, using the /give command will only give you a pig spawner.