San Francisco Giants After his junior year, the
San Francisco Giants selected Woods in the eighth round of the
2016 Major League Baseball draft. Woods signed with the Giants rather than return to Albany for his senior year. He spent his first professional season with both the
Arizona League Giants and the Low-A
Salem-Keizer Volcanoes, posting a combined 1–2 record and 3.34 ERA in 35 total innings. In 2017, he played for the Single-A
Augusta GreenJackets, going 6–7 with a 2.95 ERA in 110 innings.
Tampa Bay Rays On December 20, 2017, the Giants traded Woods,
Denard Span,
Christian Arroyo, and
Matt Krook to the
Tampa Bay Rays in exchange for
Evan Longoria and cash considerations. He did not pitch in 2018 due to injury. Woods returned to pitch in 2019, spending the year with the High-A
Charlotte Stone Crabs and compiling a 9–3 record with a 1.88 ERA over 18 games (12 starts), striking out 79 over innings. On July 21, 2020, Woods was returned to the Rays organization, but was traded back to the Royals the same day in exchange for a player to be named later. The Royals sent outfielder Michael Gigliotti to Tampa Bay on September 12 as the PTBNL. He did not play a minor league game in 2020 since the season was cancelled due to the
COVID-19 pandemic. He was assigned to the Double-A
Northwest Arkansas Naturals to begin the 2021 season. Woods split the 2022 campaign between Northwest Arkansas and the Triple-A
Omaha Storm Chasers, accumulating a 4.28 ERA with 75 strikeouts across 41 relief appearances. He elected free agency following the season on November 10, 2022.
Long Island Ducks On April 5, 2023, Woods signed with the
Long Island Ducks of the
Atlantic League of Professional Baseball. He was named the ALPB Co–Pitcher of the Month for April/May alongside Mitch Lambson of the
Southern Maryland Blue Crabs. Woods made 11 total starts for the Ducks, registering a 7–2 record and 3.77 ERA with 60 strikeouts in innings pitched.
Fubon Guardians On July 5, 2023, Woods's contract was purchased by the
Fubon Guardians of the
Chinese Professional Baseball League. In 3 starts for Fubon, he struggled to an 0–2 record and 12.54 ERA with 3 strikeouts across innings pitched. On August 30, Woods was released by the Guardians.
Long Island Ducks (second stint) On March 26, 2024, Woods signed with the
Long Island Ducks of the
Atlantic League of Professional Baseball. In 16 starts for Long Island, he compiled a 5-5 record and 5.29 ERA with 82 strikeouts over 80 innings of work. Woods became a free agent following the season. On July 7, 2025, Woods revealed that he had been injured in a car crash during the 2024 season, and would miss the 2025 campaign after undergoing surgery.
Staten Island FerryHawks On April 18, 2026, Woods Jr signed with the
Staten Island FerryHawks of the
Atlantic League of Professional Baseball. ==International career==