Rice's professional career began in 1996 with a single U.S. F2000 start, finishing eighth from second on the grid. In 1997 he raced in F2000 with Lynx Racing/DSTP Motorsports, finished fourth in points, and won the Valvoline Team USA Scholarship, representing the United States in Europe's Nations Cup. A win from pole at Nazareth in 1998 highlighted his Toyota Atlantic campaign, and in 1999 he finished fifth in the championship driving for Lynx Racing. Rice won the 2000 Toyota Atlantic Series championship, which brought him to the attention of Red Bull Cheever Racing.
Rice made his IRL debut in August 2002 at Michigan International Speedway for Red Bull Cheever Racing, filling in as an injury replacement. He lost the race by the narrowest of margins to Tomas Scheckter but made an immediate impression, completing the final five races of the season with four top-ten and two top-five finishes. In 2003 he competed in thirteen of sixteen races for Red Bull Cheever Racing before being replaced by the more experienced Alex Barron, though a call from Bobby Rahal to replace the injured Kenny Bräck at Texas Motor Speedway changed his trajectory.
In 2004, Rice started from pole and won a rain-shortened Indianapolis 500 — his first IndyCar victory. He finished third in the IRL championship that year, earning five pole positions, three wins, and leading 342 laps. For 2005 Rice was joined at Rahal Letterman Racing by Danica Patrick, but a practice crash at Indianapolis left him unable to race, with Bräck substituting in an ironic reversal of the previous year.
The 2006 season began tragically when teammate Paul Dana was killed in final practice at Homestead-Miami Speedway; Rice and Patrick immediately withdrew from that race. Rice's 2006 Indianapolis 500 ended in a crash with Helio Castroneves. He moved to Dreyer and Reinbold Racing for 2007, capturing three top-five finishes in the season's first half and finishing ninth in points — his best championship result since 2004. He was retained for 2008, posting a best result of fourth at Watkins Glen, and finished sixteenth in points. After being released at the end of 2008 his IndyCar career wound down, though he returned for the 2011 Indianapolis 500 with Panther Racing, sharing duties with J.R. Hildebrand.
Alongside his IndyCar commitments Rice maintained a parallel career in sports car racing. He debuted in the Grand-Am Rolex Sports Car Series in 2000, finishing second at Watkins Glen, and collected further podium results in subsequent seasons. He contested the 24 Hours of Daytona from 2005 to 2008 before winning the 2009 edition for Brumos Racing in a Riley Porsche. He raced full-time for Spirit of Daytona in the 2010 Rolex Sports Car Series, contributing to the team's first podium at the Six Hours of the Glen, and made his final Grand-Am appearance at the 2011 24 Hours of Daytona.
Rice also drove for A1 Team USA in the opening rounds of the 2007–08 A1 Grand Prix season before ceding his seat to Jonathan Summerton.
Away from racing Rice collects and restores classic cars. After his 2004 Indianapolis 500 victory his sponsors offered to buy him any car he chose; he selected a 1949 Mercury Eight. He has a daughter, Mina, born April 9, 2008.
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