*Club domestic league appearances and goals, correct as of 07:03, 15 August 2022 (UTC) ‡ National team caps and goals, correct as of 20:26, 5 June 2024 (UTC)
Rodák began his career in his homeland with MFK Košice before being offered a trial with Fulham in 2013. He was signed permanently by the Fulham Academy in July 2013 at the age of 16. Despite his young age, he became part of the Under-18 side and played in the 2014 Final of the FA Youth Cup against Chelsea.[3]
A short two-month loan to Farnborough in January 2015 was followed by a progression to Fulham's Under-21 side. On 15 January 2016, he joined Welling United on loan for the remainder of the season.[3] Rodák joined Accrington Stanley on loan from Fulham until the end of the 2016–17 season in January 2017.[4] He made his English Football League debut on 14 January 2017 against Cheltenham Town at Whaddon Road.[5] Rodák had a significant role in Accrington Stanley's move from the relegation zone to a comfortably mid-table position, courtesy of a 13 match unbeaten run.[3]
Rodák made his Fulham debut in a League Cup tie against Wycombe Wanderers on 8 August 2017.[6] Later that month Rodak joined Rotherham United on loan for the rest of the season[7] and made his debut in a 3–2 win at home to Bury.[8] He then re-joined the club for a further season-long loan on 25 July 2018.[9]
Rodák made his Premier League debut on 12 September 2020 in a 0–3 loss to Arsenal in the first round of 2020–21 season.[10] He then spent the rest of the season as a backup for Alphonse Areola and made only one additional league appearance in 0–2 loss to Newcastle United on the last day of the season.[11]
Rodák made his 2022-23 Premier League debut on 6 August, playing the entire 2–2 home draw against Liverpool.,[12] but was relegated to second-choice goalkeeper following the arrival of Bernd Leno from Arsenal.
On the 5th of June 2024, Fulham announced that Rodák would be leaving the club following the expiry of his contract, ending his 11-year spell at the club.[13]
On 25 July 2024, Rodák joined Saudi Pro League club Al-Ettifaq on a three-year deal.[14]