He is a two-time Olympian, a multiple-time Lithuanian record holder in the men's backstroke, freestyle and butterfly, and a double swimming champion at the 2017 Summer Universiade in Taipei, Taiwan.

Rapšys is also a member of Panevežys Žemyna Club, and is coached and trained by Ina Paipelienė.

At the 2013 FINA World Junior Swimming Championships in Dubai, United Arab Emirates, Rapšys competed in 4×100 metre mixed medley with Rūta Meilutytė, Povilas Strazdas, Eva Gliožerytė.

[2] Rapšys won gold medal in the 200 metre freestyle finals, with a time of 1:45.75, and broke the national Lithuanian swimming record.

[4] At the 2022 World Short Course Championships, contested in December at Melbourne Sports and Aquatic Centre in Melbourne, Australia, Rapšys won the bronze medal in the 400 metre freestyle with a time of 3:36.26, which was less than two seconds behind gold medalist Kieran Smith of the United States.