Originally drafted by the California Angels in the 3rd round of the 1975 Major League Baseball Draft, Lansford became the Angels' best rookie in 1978 and finished third in the overall AL Rookie of the Year vote. The Angels dealt Lansford to the Red Sox after the 1980 season. In 1981, he won the American League batting title in the strike-shortened season, becoming the league's first right-handed hitter to do so in 11 years. However, the emergence of Wade Boggs resulted in the Red Sox sending Lansford to Oakland in a trade involving Tony Armas during the 1982 off-season. Lansford became the A's third baseman for their 1988 through 1992 dynasty, typically hitting second behind Rickey Henderson. Lansford narrowly missed winning his second batting title in 1989 with a .336 average to Minnesota's Kirby Puckett, who finished with a .339 average. Although his power numbers dropped off during those years, and he missed almost all the 1991 season, Lansford's speed and solid hitting made him a significant contributor. He played in three World Series with the A's, losing in 1988, 1990 and winning in 1989.
Lansford was a hitting coach for the San Francisco Giants during the 2008 and 2009 seasons. Lansford had been relieved of his duties following the 2009 season. Lansford was hired by the Rockies for the 2011 season.
His son, Jared, was drafted by Oakland in the second round of the 2005 Amateur Draft. His other son, Josh, was a third baseman in the Chicago Cubs minor league system. His brother, Jody Lansford, spent nine seasons in the minor leagues, briefly breaking into the Big Leagues with the San Diego Padres, for whom he recorded 30 ABs in parts of two seasons, with one career home run.
He played for the Briarwood Little League team, from Santa Clara, California, which made it to the finals of the 1969 Little League World Series. In the final game of the World Series on August 2, Carney's team was defeated 5-0 by the team from Taipei City, Taiwan. Lansford is one of less than a dozen men who have played in both the Little League World Series and the MLB World Series.
Lansford went to Wilcox High School in Santa Clara, California. He also gave his name to Wilcox High School's baseball field. The field is currently called Carney Lansford field. Lansford has not played on the field as it was not built during his time at Wilcox.