Rodriguez began his youth career with Houstonians FC, a youth soccer team in Houston, Texas. He joined the Houston Dynamo academy in 2011 at the age of 15. Rodriguez played in 83 US Soccer Development Academy games while with the Dynamo academy, scoring 18 goals. He was named as the Dynamo Academy Players' Player of the Year in both 2012 and 2013. Rodriguez also trained with the Dynamo first teams for spells during the 2013 and 2014 seasons.
Professional
On December 4, 2014, Rodríguez signed a homegrown contract with the Houston Dynamo, making him the sixth homegrown signing in club history. On March 20, 2015, it was announced that Rodríguez had been sent on loan to the Dynamo's USL affiliate club Charleston Battery. He made his professional debut the following day in a 3–2 victory over Toronto FC II. Rodriguez scored his first professional goal in a 1-1 draw with New York Red Bulls II on April 18. However he would struggle the rest of to find playing time and produce the rest of the year. Ahead of the 2016 season Rodriguez was released by the Dynamo and signed a contract with USL club Rio Grande Valley FC Toros, who had replaced the Battery as the Dynamo's USL affiliate club that offseason. He made his Toros debut on March 26 in a 2-0 defeat to the Tulsa Roughnecks. Rodriguez would score his first goal for RGVFC on May 21, as he found the back of the net twice in a 4-0 win over Swope Park Rangers. He enjoyed a successful season with the Toros and head coach Wilmer Cabrera, as Rodriguez scored 6 and recorded 7 assists in 30 games to help the Toros make the USL Playoffs. On March 1, 2017 Rodriguez resigned with the Dynamo and reconnected with Wilmer Cabrera, who had taken over as coach for the Dynamo during the off-season. On April 8, 2017 Rodriguez came on as a sub in a 2-0 win over the New England Revolution to make his MLS debut. He scored his first goal for the Dynamo on June 14 in the US Open Cup vs North Carolina FC; scoring in extra time to give Houston a 3-2 win. Rodriguez scored his first MLS goal in a 3-1 win over the Montreal Impact on July 5, 2017, He would make nine appearances, most as a sub, as he helped his hometown team make it back to the MLS playoffsfor the first time since 2013. Rodriguez would not see the field in the playoffs however. Opportunities would be limited with the Dynamo for the start of 2018. After getting one appearance and 12 minutes total through the first six games, Memo was sent to RGVFC for a game, where he promptly scored. Rodriguez returned to the Dynamo after the game and he scored his first goal for the Dynamo of the season on May 5. Memo headed in a rebound in the 90th minute to give the Dynamo a 3-2 win over the LA Galaxy. Rodriguez scored a brace in a 5-0 win over NTX Rayados in the US Open Cup on June 7. The Dynamo went on to win the Open Cup, the first in club history, with Rodriguez playing in every game and getting 3 goals and an assist. Rodriguez made his CONCACAF Champions League Debut on March 5, 2019 when he came on as a sub in a loss against Tigres UANL. In the Dynamo's next match, Memo got the start against Montreal and scored on a short from 22 yards out. His strike was named MLS Goal of the Week. Rodriguez followed that up with a brace, including the game winning goal, against the Vancouver Whitecaps and a goal against the Colorado Rapids in Houston's next 2 league games. He picked up his first assist on season on May 4th in a 2-1 win over Texas Derby rival FC Dallas. Rodriguez added another assist on May 15 in a 1-1 draw with the Portland Timbers. On May 18, Rodriguez would score to help the Dynamo secure a 2-1 win over D.C. United. After appearing in a 1-1 draw with Sporting Kansas City on June 1, he missed around 2 months due to a hamstring injury. Rodriguez made a rehab appearance with RGVFC on July 13 before returning to the Dynamo lineup on July 20, picking up an assist in a 3-1 win over Toronto FC. Houston had 1 win and 6 losses during the 7 MLS games while Rodriguez was out injured. His return to the lineup was unable to save the season as the Dynamo missed out on the playoffs despite the best start in club history. Rodriguez was named as the Dynamo Young Player of the Year for his strong season, scoring 7 and assisting 5 in 26 MLS appearances.
Personal life
Rodriguez is of Mexican heritage. He grew up in El Campo, Texas. His mom would drive him over an hour each way for 12 years so he could play clubsoccer at a more competitive level in Houston. Rodriguez has 3 younger brothers.
