Having been drafted by the Edmonton Oilers in the second round, 46th overall, at the 2010 NHL Entry Draft, on 25 April 2011, the Oilers signed Marinčin to a three-year, entry-level contract.[3] During the 2013–14 season, Marinčin was called up to the Oilers, and on 5 December 2013, he made his NHL debut in a game against the Colorado Avalanche.[4]
On 5 October 2017, Marinčin was placed on waivers by the Maple Leafs.[6] After clearing waivers the next day, he was loaned to the Maple Leafs' American Hockey League (AHL) affiliate, the Toronto Marlies.[7] On 17 December 2017, he was recalled to the Toronto Maple Leafs after Nikita Zaitsev was placed on the injured reserve with a lower-body injury.[8] Marinčin appeared in two games with the Leafs before being sent down to the Marlies on 5 January 2018.[9]
On 29 June 2019, Marinčin agreed to a one-year $700,000 contract extension to remain with the Maple Leafs.[10] On 10 January 2020, Marinčin agreed to another one-year $700,000 contract extension to remain with the Maple Leafs.[11]
After six seasons within the Maple Leafs organization, Marinčin left as an impending free agent, returning to Europe in signing a one-year contract with the Czech club, HC Oceláři Třinec of the ELH, on 16 June 2021.[12]
Marinčin was chosen to play for Slovakia at the 2011 World Junior Championships. During a game against the United States, he was ejected for a hit to the head on forward Jason Zucker. This ejection carried an automatic one-game suspension, and after a review of the play, Marinčin was suspended for an additional three games.[13]