When do you say whoever or whomever?
Whoever wants the job can have it or Whomever wants the jobs can have it.
If the sentence is,
John wants the job, (so let him have it.)
you can see that John is the subject of the sentence (and 'job' is the object).
Similarly, in your original sentence:
Whoever wants the job can have it.
'whoever' is the subject of the sentence.
The subject of a sentence takes the nominative case, as in she, he, whoever
and the object of a sentence takes the objective case, as in her,him, and whomever.
Prepositions also take pronouns in the objective case, so 'whomever' would be correct in the sentence:
I'll sing whatever I like to whomever I like.
Whomever is never directly followed by a verb. Knowing about this, you'll never be lost which one to choose.