Argyle boss Paul Sturrock said: "I am very pleased. Alan Judge showed a commitment to the football club last year - his zest and enthusiasm was a benefit to us and helped take us over the final hurdle. He scored a couple of goals for us as well."
In all, the young Irishman made 17 appearances and scored two goals in his first spell at Argyle after making his debut in the 0-0 draw at Ipswich.
He has established himself as a regular in the Republic of Ireland Under-21 set-up and has earned himself seven caps, scoring one goal.