From 1994 to 1997, Parque attended UCLA and led the Bruins to the College World Series in 1997. Parque earned second-team Smith Super Team honors in his sophomore season in 1996. In his junior year, Parque was voted first-team All-American by Baseball America, first-team All-Pac-10 Conference, second-team by the Sporting News, second-team by the American Baseball Coaches Association, and third-team by Collegiate Baseball. Parque is one of the most decorated pitchers in UCLA Baseball history. He currently ranks second in career games started with 50, second in career total innings pitched with 334 innings, second in career strikeouts with 319, third in career pitching wins with 25, and seventh in career complete games with 10. In terms of single season pitching records for the Bruins, Parque ranks third in wins with 13 in 1997, ninth for games started with 19 in 1997, ninth for innings pitched with 125 in 1996, fourth in strikeouts with 119 in 1997, and fifth in strikeouts with 116 in 1996.
In the supplemental draft, he was drafted by the Chicago White Sox in the 1st round. Parque made his major league debut the following year, pitching in 21 starts for the White Sox. He had an ERA of 5.10 with a 7-5 record in 113 innings. In 1999, Parque finished the season with a 9-15 record in 30 starts. He enjoyed his best season in, going 13–6 with a 4.28 ERA in 33 games. The 2001 season saw Parque pitch in 5 starts only after suffering a shoulder injury, which sidelined him for the rest of the season. Parque began the 2002 season in the minors building uparm strength after his 2001 shoulder surgery. Parque was not the same after shoulder surgery, his 2002 season saw him pitch to an ERA of 9.95 in 8 games while walking 16 batters in just 25 innings. Parque was let go after the 2002 season. After numerous shoulder injuries between 2001 and 2002.
Parque signed a minor league with the Devil Rays in 2003. He was released after posting a whopping 11.94 ERA in 5 starts.
Arizona Diamondbacks
In January, 2004, Parque signed a minor league deal with the Diamondbacks. On June 24,, he announced his retirement after playing seven seasons of professional baseball due to his recurring arm injury from.
Return to baseball
After being out of baseball for three years, Parque announced his willingness to return to the game of baseball. He started his return by instructing lessons for the Cook County Cheetas in Oak Lawn. The Chicago Tribune reported that he threw his fastball in the range of 90 mph. On February 2,, he signed a minor league contract with the Seattle Mariners. He was released by Seattle on May 31, 2007. He has since been linked to steroids in December 2007, though he denied the account in the Seattle Times. In a July 23, 2009 article in the Chicago Sun-Times, Parque admitted using human growth hormone while rehabbing from a shoulder injury in 2003. At the time, HGH had not yet been banned by MLB.