Parkin won caps for England while at Wakefield Trinity in 1921 against Wales, Other Nationalities and Australia, in 1922 against Wales, in 1923 against Wales, in 1924 against Other Nationalities, in 1925 against Wales, in 1926 against Wales and Other Nationalities, in 1927 against Wales, in 1928 against Wales (2 matches) and won caps for Great Britain while at Wakefield Trinity in 1920 against Australia (2 matches) and New Zealand (3 matches), in 1921-22 against Australia (2 matches), in 1924 against Australia (3 matches) and New Zealand, in 1926-27 against New Zealand (2 matches), in 1928 against Australia and New Zealand and in 1929 against Australia (2 matches).
Parkin was unavailable for the first Test of the 1929/30 Ashes series and the game was lost to the touring Australians. He recovered for the second Test and Great Britain ultimately defended the Ashes. Parkin decided he wanted to leave the Wakefield club in 1930, at the age of thirty-four, and he was put on the transfer list at £100 (based on increases in average earnings, this would be approximately £15,950 in 2013). For some reason, Hull Kingston Rovers couldn't, or wouldn't, find the money. So Parkin paid the fee himself to secure his release. The game's by-laws were adjusted shortly afterwards, so that no player could ever do that again.