He was drafted by Sydney with their third selection and fifty-sixth overall in the 2015 national draft.[3] He made his debut in the one point loss against Collingwood at the Sydney Cricket Ground in Round 3 of the 2017 season.[4] After spending long periods of time playing in the NEAFL for Sydney, Dawson began to find form in 2020 at a time when the Swans were struggling. Dawson impressed rival clubs in his last game for Sydney, which was the 2021 elimination final against Greater Western Sydney. Dawson had 18 disposals and 8 marks in the narrow loss.[5]
2024 began with scrutiny directed at Jordan Dawson, with Adelaide's 0-4 winning record "epitomised" by Dawson's poor form.[10] Dawson responded with back-to-back best-on-ground performances against Essendon and North Melbourne, the latter of which saw Dawson awarded with the ANZAC Spirit medal, given to the player adjudicated best-on-ground during the AFL's ANZAC Appeal Round.[11] Dawson was forced to miss one game in the season following a head collision with Essendon forward Nate Caddy.[12] His absent leadership was noticeable in a large loss to Hawthorn the following week. Despite the Crows once again missing finals, Dawson strung together some good form to lead the club in coaches' votes[13] as well as in Brownlow votes for the second year in a row. Dawson won consecutive Malcolm Blight Medals, being a part of the first tie in the history of the award alongside Ben Keays. He was also awarded with Adelaide's Players' Trademark Award for the second year in a row.[14]
^The 2020 season was played with 17 home-and-away matches per team (down from 22) and 16-minute quarters with time on (down from 20-minute quarters with time on) due to the impact of the COVID-19 pandemic.