'How many cups of coffee have you drunk (so far) today?' This is a correct sentence. However, it would be more common to say 'How many cups of coffee have you had (so far) today?' which sounds more natural just because it's more common.

I think it is okay except for one thing. The verb "drink" is generally used in association with consumption of alcoholic beverages. So, the better sentence can be like this: How many cups of coffee have you had today?

"How many cups of coffee have you had so far today?" "How many cups of coffee have you drunk today?" <== also looks fine

It's perfectly correct. The only thing wrong is the missing capital letter at the beginning of the sentence.