Rodriguez began his collegiate career at Kansas State. As a sophomore, he averaged 11.4 points and 5.2 assists per game. Following the season, he opted to transfer to Miami (Florida) to be closer to his home in Puerto Rico.[2] Rodríguez averaged 12.6 points per game, 1.7 steals per game and 4.5 assists per game as a senior. On March 6, 2016, Rodríguez was named to the Third-team All-ACC.[3] He also led his team to the Sweet 16 of the NCAA tournament.
On August 3, 2017, Rodríguez signed with the Israeli club Maccabi Haifa for the 2017–18 season.[7] On May 7, 2018, Rodríguez recorded a career-high 31 points, shooting 4-of-5 from three-point range, along with 4 assists and 3 steals in a 92–79 win over Maccabi Rishon LeZion.[8]
In 31 games played during the 2017–18 season, Rodríguez led the Israeli League in steals (2.4 per game) and was the fifth leading player in assists (4.7 per game). Rodríguez also averaged 13.1 points and 3.5 rebounds per game.
On 2020, Rodriguez Tricoche returned to the Baloncesto Superior Nacional to play for the Vaqueros de Bayamón. On March 12, 2020, the league announced that they will be postponing the tournament because of the coronavirus. The BSN resumed the competition on November 10, 2020, in a bubble format, similar to what the NBA did. The bubble took place at the Wyndham Grand Rio Mar Puerto Rico Golf & Beach Resort, in Rio Grande, Puerto Rico with a duration of six weeks. The Vaqueros were crowned champions after sweeping the Piratas de Quebradillas in the Serie Final Chrysler. Angel carried the finals Most Valuable Player award after helping Bayamon to won their 15th championship in league's history.
The next season, even he was named Most Valuable Player and dominated the league with 19 points, 5.6 rebounds, and led the tournament in assists averaging 8.4 per game, not everything were good news for the team. On September 27, 2021, the point guard injured his right hand thumb and that kept him out for the rest of the season. The Vaqueros still went to the playoffs but were eliminated in the semifinals by the Mets de Guaynabo (basketball).
In the 2022 season, he won his second championship with Bayamón when they defeated Atléticos de San Germán in the finals.
Rodríguez played for Puerto Rico at the 2017 FIBA AmeriCup where he averaged 10.7 points, 3.3 rebounds, 2.0 assists and 2.3 steals per game in two games played.