The word 'job' is a singular countable noun, like 'pen' or 'book', so it needs an article (a/the) or another determiner (e.g. your, this) before it. It cannot stand alone.
Only uncountable nouns, such as 'tea' 'work' or 'furniture', can be used without an article in the singular.
You cannot omit the word 'a' - this is why "What do you do for job?" is definitely wrong.
"What do you do for a job?" is better, but it isn't a natural way to ask this question. Here are some standard questions:
"What do you do?"
"What do you do for a living?"
"What's your job?"