In the 1970s he played successively for Quilmes, Club Atlético Tucumán and Racing Club. At the 1978 FIFA World Cup, he was a member of the Argentinian team that won the tournament and made two appearances as a substitute in the second round. Afterwards, he was snapped up by Tottenham's Keith Burkinshaw together with Ossie Ardiles.
Arriving to a ticker tape welcome at White Hart Lane, Villa scored one goal against Nottingham Forest on his debut. Villa scored 18 goals in 133 Spurs appearances, none more spectacular than his winning goal against Manchester City in the FA Cup Final replay in 1981 - for which he won the Wembley goal of the century award in 2001. He had also opened the scoring in the 8th minute of that final replay. Today, Spurs fans recall Ricky's unique contribution wearing t-shirts with his hirsute visage morphed into Che Guevara's.
Villa played on in the United States, Colombia and Argentina before ending his career in the lower leagues of Argentine football with Defensa y Justicia.
Villa also represented Argentina in the 1991 edition of the World Cup of Masters, scoring in the opening round against England.
He dedicated himself to politics during the 1990s, but since July 2005 has been the technical secretary of Talleres de Córdoba. He resides in Villa Carlos Paz with his wife and four children. As of November 2007, it was announced by FIFA that all members of winning World Cup squads prior to 1982 would receive World Cup winners medals and this includes Villa as part of the 1978 World Cup winning squad.
On February 7, 2008 Ricky Villa along with his compatriot Ossie Ardiles was inducted into the Tottenham Hotspur Hall of Fame