What exactly do you mean by 'Do you drink some juice?'?
If 'some' means the type of juice is unknown or unimportant, i.e. 'I drink some sort of juice', than you can use «како́й-то»: «Я пью како́й-то сок».
If 'some' is about the quantity, then 'some' can be translated with «немно́го» 'a little', but it sounds weird in the present tense. 'Some' describes the quantity, but the quantity cannot be measured in Present tense: it's either something you've already drunk (and then you use the Past tense), or something you’re going to drink (and then you use the Present tense). For the same reason you cannot use Genitive/Partitive case in this sentence.
We don't usually use partitive with imperfective verbs (and only imperfective verbs have the present tense form).
Partitive roughly means "some", it basically refers to quantity. However, how do you measure a quantity of something that's in progress? You either measure the quantity of what you've drunk (and then you use the perfective verb in the past tense), or the quantity of what you're planning to drink (and then you use the perfective verb in the future tense), but you can't measure the quantity of what's going on. At least from the point of the Russian language.
Upd.: oh, sorry, it seems I've just repeated what I've said a month ago. :D Anyway, I can't provide you with a better explanation. We just don't use genitive objects with imperfective verbs, it just sounds wrong.