Rodriguez started his youth career with FC Dallas. However, his road through the academy system was not cut and dried.[1] Rodriguez was actually rejected the first time he tried to join the FC Dallas academy.[1] After this rejection, Rodriguez played for FC Dallas youth coach Victor Medina outside of the FC Dallas academy for three years.[1] His career took off when Rodriguez starred for his club against professional youth sides from Mexico, like C.D. Guadalajara and Club León.[1] From that point, Rodriguez signed for FC Dallas's academy in 2017. He helped the club win the prestigious Dallas Cup during his time with the academy.[1]
Professional
On January 31, 2019, Rodriguez signed his first professional contract with North Texas SC, the reserve team of FC Dallas, in USL League One.[2] Rodriguez's younger brother, David Rodriguez, was also signed to a professional contract with the club.[3] Rodriguez made his debut on March 30, 2019, in a 3–2 win against the Chattanooga Red Wolves.[4] Rodriguez helped lead North Texas to the USL League One2019 regular season and post-season championship, while becoming the league's assist leader with 10 assists and a leading MVP candidate.[5][1] On October 31 and November 1, respectively, Rodriguez was named both the Young Player of the Year and the League's Most Valuable Player (MVP).[6] He scored his first goal for the club on November 5, 2019, against fellow MLS reserve side Orlando City B.[4]
Rodriguez signed with Phoenix Rising FC on December 8, 2020, and left on January 23, 2023.[7][8]
Rodriguez was signed by the Charleston Battery on March 24, 2023, to a one-year deal with an option for an additional year.[9] Joining shortly after the start of the 2023 season, Arturo enjoyed ample success in his first year with the Battery. His first goal came on April 8 with one of the last kicks of the match against Hartford Athletic, securing Charleston the victory amid heavy rainfall. Rodriguez scored four goals and five assists across 27 Championship matches and led the team in chances created (44). Rodriguez provided heroics in the playoffs with two goals and two assists, including a goal in the Eastern Conference Final against Louisville City FC to knock out Louisville and win the conference title. Charleston would end runners-up in the USL Championship Final.
In 2024, Rodriguez's contract option was picked up by the Battery and he switched his number from 12 to 10.[10]