On 25 August 2012, Tettey signed for Premier League club Norwich City on a two-year deal for an undisclosed fee. He scored on his debut, scoring the only goal of the game in a 1–0 win against Doncaster Rovers on 26 September in the League Cup. He was also named man of the match, and stated he hoped his performance had been enough to earn him a start in a Premier League game. He made his league debut three days later, replacing Steve Morison in the 79th minute of a 5–2 defeat against Liverpool at Carrow Road. He made his first league start on 6 October against European champions Chelsea, however he could not prevent Norwich falling to a 4–1 defeat after Grant Holt had given the Canaries an 11th-minute lead. He made his full home debut on 20 October, helping Norwich to a shock 1–0 win against Arsenal after another goal from Holt. He became a regular in the team until he suffered an injury in February 2013, which persisted and kept him out of action for a longer period than initially thought. After over a month out, he made his return to playing on 30 March, replacing Jonny Howson in the 85th minute of a 1–0 defeat away to relegation rivals Wigan Athletic. He played in the final game of the season on 19 May, as Norwich produced a shock result to beat Manchester City 3–2 at the City of Manchester Stadium, to inflict only their second home defeat in the last 48 games, and to give Norwich their highest Premier League finish of 11th since they finished third in the 1992–93 season.