It sounds horribly odd to my ears (probably worth noting the group in that song is not native-English speaking). Crave is (virtually) always a transitive verb in Modern English and needs to have an object. The reason that the noun form works with for is that nouns will need prepositions to add in objects like that. For example, The company prints Ø the books versus There's a new printing of the books.
As Peter Shore points out, the OED recognizes its use, but its usage is quite rare these days. Searching around with some other phrases besides I crave for (since that's taken up by song lyrics), almost every instance of crave for sounded off to my modern ears except when for was the head of a clause or when the object craved is intended for someone else:
- Someone craves for someone else something.
- in other words: Someone craves something for someone else.
- I crave for someone to do something.
- but not *I crave someone to do something.
For examples of these you've got Rest he craves for you in His bosom 1
- …he craves for you to f— off 2
So you can use it as it's certainly been used that way, but recognize it will come off as antiquated or weird to most people.