Learn Danish: Du virker træt.

Yes, that is a very common meaning! For example, tv'et virker ikke means 'the TV doesn't work'. However, when describing people or situations, virker often means 'seems' or 'appears'. In this sentence, Du virker træt translates to 'You seem tired'.

Why is the adjective træt used without an 'e' at the end?

Because it describes the subject Du (you), which is singular. In Danish, adjectives must match the noun or pronoun they describe. If the sentence was about plural 'you' or 'they', it would be I virker trætte or De virker trætte.

Could I say Du ser træt ud instead?

Absolutely. Du ser træt ud means 'You look tired,' which is very close in meaning. Du virker træt ('You seem tired') is just slightly broader, as it could be based on how the person is acting or talking, not just their physical appearance.