Born in Nasugbu, Batangas, Tenorio attended the Ateneo de Manila University, the Jesuit-run institution known for its tough academic regime as well as its burgeoning college basketball program. Tenorio made an immediate impact as a rookie for the Blue Eagles of Ateneo de Manila as he helped lead his team into the 2001 basketball Finals of the University Athletic Association of the Philippines (UAAP). Tenorio was practically unstoppable in Game 3 of the Best-of-3 Finals Series as he scored 30 points against their college rival De La Salle University-Manila. DLSU-Manila however would go on to win that series.
The following year, in 2002, Tenorio would once again lead the Ateneo de Manila back to the UAAP Finals. This time he and his team would not be denied as they exacted vengeance on DLSU-Manila to win the UAAP Men's Seniors basketball championship.
Tenorio would make a third straight Finals appearance in 2003 but he and his Blue Eagle team would yield their crown to the veteran Far Eastern University Tamaraws.
Tenorio played a total of five seasons with Ateneo de Manila and also graduated with a Bachelor of Arts degree in 2006, something he considers a far more important achievement than any of the basketball accolades he ever got. He played under four college coaches: Joe Lipa, Joel Banal, Sandy Arespacochaga and Norman Black.
After completing his collegiate eligibility he then saw action in the quasi-commercial basketball league of the Philippines, the PBL (Philippine Basketball League) the last stepping stone towards achieving a professional basketball career. In his last PBL Conference he led his Harbour Centre Portmasters team to the 2006 PBL Unity Cup championship, a fitting end to his career as an amateur player.
In the 2006 Rookie Draft Tenorio was the 4th over-all draft pick by the San Miguel Beermen. He played an average of 25.5 minutes for Magnolia with a respectable average of 7.8 points, 4.6 assists and 3.6 rebounds in nine games.
In a surprise move in March, 2008 the Alaska Aces traded Mike Cortez and Ken Bono for Magnolia’s LA Tenorio and Larry Fonacier. The Aces have been happy with the trade as they got a pure point guard in Tenorio to make life easier for Willie Miller who could now concentrate on his scoring.
In the first four games of the 2009-2010 KFC-PBA Philippine Cup Tenorio has not disappointed the Alaska expectation. As a starting point guard Tenorio led the Alaska team to a scrambling victory over San Miguel Beer in their first game. In their next three games Tenorio was ever the reliable point guard who led his team to the top of the standings in the PBA.
In August 31, 2012, Tenorio was traded to the Barangay Ginebra San Miguel in a six-player blockbuster deal.
Tenorio made his name on the final list of the Smart Gilas 2.0 roster. The first tournament of the Gilas were the prestigious 2012 William Jones Cup which was held from August 18–26 in Taipei. The Gilas makes a 6-1 record, before battling out the USA Team for their last game. Tenorio led the team to beat the USA team 76-75, finishing with 20 points and grabbing the most important rebound of the game. The Gilas won the tournament with a 7-1 record, and the 4th championship of the Philippines in the Jones Cup. Tenorio eventually became the tournament's Most Valuable Player after his last performance against the tough USA Team.