Snodgrass signed for Norwich City on a three-year contract in July 2012 for an undisclosed fee. He made his debut in the opening game of the season on 18 August 2012, a 5–0 defeat away to Fulham. Two matches later, on 1 September 2012, Snodgrass scored his first goal for the club when he scored the equaliser which saw Norwich draw 1–1 with Tottenham Hotspur. He scored his second goal on 28 November, scoring a free-kick in a 1–1 draw against Southampton.