As a member of Karakán KK, Péter Szittya was one of the pioneers of kayaking in Hungary. In the unofficial Hungarian championship in 1936 and 1937, he finished first in K1 at 1,000 and 10,000 metres. In 1936, along with several of his teammates, he took part in the Berlin Olympics at his own expense, where he did not reach the final in K1-1000 and placed 12th in the K1-10K. After the Olympics he continued to win competitions in Hungary. In 1942 together with other kayakers he founded the kayak department of MOVE and continued his career with this new affiliation. In 1943 Szittya finished first in the first ever (and probably last) Eskimo rotation competition in Hungary when he made 26 turns in 20 minutes.
Hungary