Alicea played for the Kansas City Royals, Texas Rangers, Anaheim Angels, St. Louis Cardinals and Boston Red Sox.

He played college baseball for the Florida State University Seminoles with his brother Edwin under head coach Mike Martin.

Despite his struggles, the Cardinals brought him back to the big leagues in 1992 and he hit .245 with a pair of homers and 32 RBI in 85 games.

He continued to improve as, in 1993, 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 1994, Alicea set a then-career high in home runs with five while hitting .278 with 29 RBI in 88 games.

In January 1997, Alicea signed a one-year deal with the Anaheim Angels, taking over at second base for Randy Velarde.

On November 29, 2006, Alicea was named by the Red Sox as their first base coach, taking over for Bill Haselman.