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Which one is the correct form?

He's prejudice against/towards women.

He's prejudiced towards/against women.

"Prejudice" is a noun. You can't be prejudice -- instead you have a prejudice.

He has a prejudice against eating what he considers "foreign" food.

Or you can say the same thing with "prejudice" as a verb, in this case expressed as a past participle adjective:

He is prejudiced against eating what he considers "foreign" food.

Both are fine. There is no difference in meaning.

He has a prejudice against women

He is prejudiced against women.

Side note: Because "prejudice" is generally a negative condition, you have to be careful when using "prejudice towards" something. This usually indicates a prejudice in the direction of some negative outcome:

The judge ruled the evidence would unlawfully prejudice the jury toward convicting the defendant.

This means that when you say something like, "He is prejudiced toward women," it implies you disapprove of this attitude. If you want to make a more neutral statement, you can instead use terms like "prefer", "incline toward", or "partial to".

Prejudice is a noun, and prejudiced is an adjective. Let's say you were to say:

He is prejudice against women.

Then you would be claiming that he, himself, is "prejudice against women", a concept or feeling or state of mind. That's a noun phrase. Being generous, we could assume you were describing him as the personification of such prejudice. That is highly unlikely to be anything you want to say.

But then there's:

He is prejudiced against women.

This is a much more sensible thing to say. In that case, prejudiced is an adjective, and against women is a complement of that adjective, as it completes the meaning of prejudiced. Actually, the against women bit is a complement in the other case as well.

Now, a quick exploration of that against/towards thing. There's an argument that prejudice is an inherently negative concept, and philosophically it might be. As a word, though, it means to pre-judge, to judge in absence of evidence based on some characteristic. There's a school of thought that says that prejudice toward(s)¹ something is prejudice in that thing's favour, and prejudice against something is to that thing's detriment.

In my experience, some people have that assumption, and others don't. Personally, I see prejudice against as to the detriment, and prejudice towards as neutral. The expression for prejudice in favour would be prejudice in favour of. NGram suggests that against is used more than the other forms put together, though in favour used to be much more common than toward(s).

¹: Let's not get into the toward/towards debate here, though. It's rather tangential to the question.

In the first usage "prejudice" is a noun, and in the second usage "prejudiced" is an adjective.

The usage as a descriptive noun might rarely be used at a stretch as

He's prejudice personified

but the usual use is as the adjective "prejudiced".

About the choice of against and toward, these two examples show the difference.

He's prejudiced against women.

He's friendly towards beggars.
e that is unlikely to be used by a native speaker.