Is judge an adverb

No. It is either a verb or a noun.

Judge as in judging something is a verb. It describes an action.

Judge as in a court judge, is a noun. It's a person.

Judge isn't an adverb, unless you change it's form to 'judgingly' as in 'He judgingly reviewed my work.' In that sentence, judgingly modified reviewed. How did he review my work? Judgingly.