He was drafted by the St. Louis Cardinals in the first round of the 1986 amateur draft. He made his major league debut in a 12–9 Cardinals loss to the New York Mets on April 23, 1988. Starting at second base and batting eighth, Alicea went 1-for-4 with a triple, a walk and a run scored in his debut. He hit.212 with one home run and 24 RBI in 93 games with the Cardinals that season. Alicea spent the next few seasons in the minor leagues before returning to the big leagues with St. Louis in, hitting.191 without a single RBI in 56 games. Despite his struggles, the Cardinals brought him back to the big leagues in and he hit.245 with a pair of homers and 32 RBI in 85 games. He continued to improve as, in, Alicea hit.279 with three home runs and 46 RBI, stealing 11 bases in 12 attempts, over 115 games. Despite a drop in playing time in, Alicea set a then-career high in home runs with five while hitting.278 with 29 RBI in 88 games.
On December 7, 1994 he was traded to the Boston Red Sox for Jeff McNeely and Nate Minchey. He played one season with the Red Sox, batting.270 with six homers and 44 RBI. Alicea was one of a few Boston players to perform well in the American League Division Series against the Cleveland Indians. He hit.600 with a double and home run as the Red Sox were swept in three games.
St. Louis Cardinals, second stint
Alicea was waived by the Red Sox, returning to the Cardinals on March 19, 1996. He hit.258 with five home runs and 42 RBI in 129 games for St. Louis.
Anaheim Angels
In January, Alicea signed a one-year deal with the Anaheim Angels, taking over at second base for Randy Velarde. In 128 games with the Angels, Alicea hit.253 with five home runs and 37 RBI, stealing a career-high 22 bases. That winter, he signed as a free agent with the Texas Rangers.
Texas Rangers
In his first season in Texas, Alicea hit.274 with six home runs and 33 RBI in 101 games. In, he hit.201 with three homers and 17 RBI in 68 games with the Rangers. It was in that he had his best season establishing career highs with a.294 average, 85 runs, 159 hits, and 63 RBI.
He played his last two seasons with the Kansas City Royals before retiring following the season. In, Alicea hit.274 with four home runs and 32 RBI in 113 games. In his final big league campaign, he hit.228 with a homer and 23 RBI in 94 games.
Coaching career
After his playing days ended, he managed the Lowell Spinners in and and was skipper of the Greenville Drive in. On November 29, 2006, Alicea was named by the Red Sox as their first base coach, taking over for Bill Haselman. He served in this position through the and seasons. On October 22, Alicea was told by manager Terry Francona that he was not going to be offered a contract. Alicea was then hired by the New York Mets to be their first base coach for the season. On October 5, 2009, after the Mets' dismal 70–92 season, they announced that Alicea would not return to the Mets coaching staff in the 2010 season.
