At Wrexham, Armstrong made his professional debut as a teenager during the 1989–90 Football League season in the old Fourth Division, and managed to score three times through the course of the season. In his two-year spell at the club, he went on to play 60 games, scoring 13 times. He took part in the 1990–91 European Cup Winners' Cup, where he scored the only goal of the first round tie against Denmark's Lyngby before elimination by eventual champions Manchester United in the second round.