Originally from Doncaster, Yorkshire, Rix joined Arsenal as an apprentice in 1974 and turned professional the year after. He made his debut for the club against Leicester City on 2 April 1977, and marked it by scoring the opening goal. Rix immediately became a regular on the left wing, replacing George Armstrong. Together with Liam Brady he formed part of an impressive attacking midfield, which helped Arsenal to three successive cup finals between 1978 and 1980. Arsenal only won one of these, in 1979 against Manchester United; the final score was 3–2, with Rix crossing for Alan Sunderland's last-minute winner, just seconds after United had equalised to level the score 2–2.
Arsenal reached the Cup Winners' Cup final the following season, against Valencia; the match finished 0–0 after extra time – a penalty shootout ensued, but Rix missed his kick and Arsenal lost. After the departure of Liam Brady to Juventus that summer, many believed Rix would also leave but he stayed at the club, and became captain in 1983. Arsenal's form slumped in the early 1980s, though, meaning Rix was unable to claim any silverware as skipper.
A series of injuries to his achilles tendon kept Rix out of the team in the mid-1980s, and he lost his starting place in the side to Martin Hayes. Rix spent a spell on loan at Brentford, before being released in 1988. In all he played 464 times for the Gunners, scoring 51 goals.
Between 1980 and 1984, Rix played for the England national team, including making five appearances at the 1982 World Cup. He was capped 17 times, but failed to score. His first appearance came on 10 September 1980 in a 4–0 win over Norway, his last in a 1–0 win over Northern Ireland on 4 April 1984.
Rix joined Chelsea as youth team coach in mid-1993; during an injury crisis, he briefly enlisted as a player for the club, playing a solitary Premier League match in May 1995 against his old side Arsenal. Rix became assistant manager in 1996 under new Blues boss Ruud Gullit, and continued in the same role under Gullit's successor Gianluca Vialli, winning the FA Cup in 1997, and the League Cup and Cup Winners' Cup in 1998.
In March 1999, Rix was sentenced to 12 months in prison, of which he served six, for having underage sex with a 15-year-old girl. He was also ordered to be placed on the sex offenders' register for 10 years, and banned by the FA from working with youth players under the age of 16. Upon his release from prison he immediately rejoined Chelsea in his old job. He won the FA Cup again in 2000 before leaving the club after Vialli was sacked by Ken Bates, after a brief spell as caretaker manager.
Rix managed Portsmouth between 2001 and 2002, where his enthusiastic style of management started well, but tapered off in the middle of the 2001–02 season. A string of poor results, including a 4–1 home loss in the F.A Cup to bottom of the Football League Leyton Orient, meant that Director of FootballHarry Redknapp was given more responsibilities until he eventually replaced Rix as team manager toward the end of the season. Rix then managed Oxford United for seven months in 2004. Their form declined sharply during the last three months of the 2003–04 Division Three campaign: they fell from the automatic promotion places to ninth in the final table, failing to achieve even a playoff place. His position was always rumoured to be 'unsafe', and he was sacked after their dismal form continued into 2004–05, where he led the club to nearer the relegation zone than the play-offs.
In November 2005, after speculation linking him with the manager's job at Scottish Premier League club Heart of Midlothian, it was confirmed that Rix would take over at Tynecastle. He officially took the position of head coach on 8 November 2005. Events reported in February 2006, by Scottish newspapers, suggested that Rix was unhappy with Vladimir Romanov's "hands on" approach and speculation increased that Romanov was involved in team selection. On 22 March 2006 Rix was sacked as manager after just four months in charge, with the club citing poor results as the reason.