The Baltimore Orioles selected Rodriguez in the first round, with the 11th overall selection, of the 2018 Major League Baseball draft.[4] On June 12, 2018, Rodriguez signed with the Orioles for $4.3 million.[5] He made his professional debut with the Gulf Coast League Orioles and spent the whole season there, going 0–2 with a 1.40 ERA in nine games (eight starts).[6][7]
Rodriguez spent 2019 with the Delmarva Shorebirds, earning South Atlantic League All-Star honors.[8][9] That July, Rodriguez represented the Orioles at the 2019 All-Star Futures Game.[10] Over twenty starts with Delmarva, he went 10–4 with a 2.68 ERA, striking out 129 batters over 94 innings.[11] Rodriguez did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[12]
To begin 2021, he was assigned to the Aberdeen IronBirds.[13] He was promoted to the Bowie Baysox during the season.[14] Over 23 starts between the two teams, he went 9–1 with a 2.36 ERA and 161 strikeouts over 103 innings.[15]
Rodriguez was assigned to the Triple-A Norfolk Tides to begin the 2022 season. On June 2, 2022, it was announced that Rodriguez would miss time with a right lat muscle strain.[16] He had compiled a 2.09 ERA in 11 starts with Norfolk at the time of his injury. On November 15, the Orioles added Rodriguez to their 40-man roster to protect him from the Rule 5 draft. [17]
On March 27, 2023, the Orioles announced that Rodriguez would not be part of the Opening Day rotation and would begin the year in Norfolk.[18] On April 4, it was announced that Rodriguez would be starting on April 5 against the Texas Rangers.[19][20] In his debut, he pitched five innings, allowing 2 earned runs on 4 hits, while striking out five, resulting in a no decision.[21][22] He went eight innings without a walk in an 8–0 home win over the Tampa Bay Rays on September 16.[23] For the season, he was 7-4 with a 4.35 ERA and 129 strikeouts across 23 starts.