If you want to keep it very formal. Informally one would say something like "Trau dich, trinks!", or even shorter, "Komm, trinks!" or "Hopp, trinks!". Also depends on the exact intentions, if it were a bet, one could translate it as "Wetten dass dus nicht trinkst?", which would also state which side of the bet the speaker is on. "Herausfordern" is also more something like "challenge", as in "one knight challenging the other", less like "dare" as in "one child trying to get the other to do something".
Shortest translation that comes to my mind would be:
"Ich fordre dich zum Trunk."
Which IMO translates the original sentence pretty well. You could add a "heraus" at the end but as a native I would not say that it is necessary. Also the Word "Trunk" sounds a bit antiquated but Duden still lists it, therefore I'd say it's fair game.
