Luka Ščuka spent his entire youth career in Nova Gorica, where he played for all the younger selections of the Nova Gorica club. Ščuka, a talented, 208 cm tall basketball player, also played in the jersey of the Gorica member team for the last two seasons, and in the 2019/20 season in the 3rd SKL he averaged 15.8 points per game and played in 15 matches. In the Spar Cup, he stepped on the floor in six games and scored 12.0 points per game. In member basketball, Ščuka tested himself mainly on the playing position of the wing, but he also likes to have the ball in his hands, and he is tested on the position of the organizer of the game.

In 2018, Ščuka played in the Slovenian national team jersey at the European Championship for boys under 16 in Novi Sad and scored 3.9 points and 2.9 rebounds. In 2019, Luka also played in the European Under-18 Championships, scoring 0.3 points and 0.5 rebounds.

In the 2020/21 season, Ščuka averaged 0.8 points, 1.6 rebounds and 0.4 assists in the regional league in Cedevita Olimpija, and 9.6 points in the Slovenian national championship, where he got more opportunities to play. , 5.6 rebounds and 1.0 assists per faceoff. In the 2021/22 season, he played in 14 games of the AdmiralBet ABA League and scored 2.2 points, 1.2 rebounds and 0.2 assists, and in the Slovenian national championship he recorded 11.7 points, 7.1 rebounds and 1.2 assists per game.

During these two seasons, Ščuka also got his chance in the 7DAYS EuroCup, where he played in nine matches so far. In the 2021/22 season, he averaged 1.4 points and 1.4 rebounds per faceoff in eight games. He also made his debut in the jersey of the Slovenian men’s national team.

Ščuka was supposed to spend the 2022/23 season as a basketball player on loan from Cedevita Olimpija in Bar pri Mornarje, and due to a knee injury, he devoted it to rehabilitation after surgery.