The Polish goalkeeper was signed from Legia Warsaw in 2019 when he was sixteen years old. Ojrzynski featured for the U18s and the U19s UEFA Youth League squad in 2019/20. He signed a professional contract in the summer of 2020 and was on the bench when Liverpool beat Sheffield United in the Premier League on 28 February 2021. He spent 2021/22 on loan at Welsh Premier League side Caernarfon Town, starting all but four of their league games.

Ojrzynski was loaned to Polish top flight side Radomiak Radom for 2022/23 but after starting just three games he was recalled during the January transfer window. He was loaned to Den Bosch in the Dutch second tier for 2023/24, making eleven appearances. In 2024/25 Ojrzynski didn't make any appearances for the U21s before joining Swedish second tier side Utskitens BK on loan in March for their summer season. He was released by Liverpool at the end of June 2025 after his contract expired and the following month he signed for Orebro, another club in the Swedish second tier.