Can a rat woman match well with a rooster man?

It may not be a good pair in the end, although you may feel good at first. You two have different approaches towards life and will quarrel a lot during daily life. Rooster is straightforward and traditional. Rat is shrewd and a bit manipulative. This kind of difference will escalate until the relationship ends or they can accept these difference.
However, I think if you love each other, everything will be solved, because the Chinese astology is not always true. So I am sure you can live a happy life.