Born in Split, Grčić began his football career in 1940 with the juniors of RNK Split, where he continued to play until 1946. In 1946 he joined the Army and for three years was a regular for JRV Naša Krila based in Zemun, playing over 300 games for the club. In June 1950 after the 1949–1950 season, the club was dissolved and Grčić joined Hajduk Split and played for the club until 1956.