After forming part of the Mexican 4 X 100 metres relay in the 1992 Summer Olympics, he opted for the decathlon.
In 1995 he earned a bronze medal in the Pan American Games in decathlon and another bronze as the member of the 4 X 100 relay.
During 1996, he specialized in the 400 m dash, in which participated in the 1996 Summer Olympics, and qualified for the semifinals, with a time of 45.33 s.
In 1998 he participated in the Central American and Caribbean Games, in 400 m dash, in which he earned a bronze medal.
Cárdenas also participated in 1999 on the IAAF World Indoor Championships, in 400 m dash in which he earned a bronze medal. That same year also participated in the World Championships in Athletics. Alejandro ran along with Michael Johnson, he reached a third place, and a personal record of 44.31 s.
Little time later he participated in which were its last Pan American Games, reaching a third place in the 400 m dash.
Alejandro participated in the 2000 Summer Olympics, in 400 m dash, running 46.14 s in the first round, and 45.66 in the semifinals, in which did not advance.
Four years later Cárdenas participated in the 2004 Summer Olympics, in the 400 m dash, running 45.46 s in the first round, and 45.64 s in the semifinals, in which did not advance.
In the 2005 the Mexican athlete again participated in the World Championships, in Helsinki, Finland, being eliminated in the first round with a time of 46.73 s.200 metres - 20.63 s (1998)
400 metres - 44.31 s (1999)
Decathlon - 7,614 points (1996)