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Horn. The drinking horn, known for centuries , was documented in use in several Viking era sagas such as the Prose Edda and Beowulf.
from wikipedia:
Horn fragments of Viking Age drinking horns are only rarely preserved, showing that both cattle and goat horns were in use, but the number of decorative metal horn terminals and horn mounts recovered archaeologically show that the drinking horn was much more widespread than the small number of preserved horns would otherwise indicate
Not to say other technologies weren't available, this one would have been readily accessible from farmer on up to king.
The other answer,of course, is that the Viking drank from whatever he plundered.