Born in Bootle, Lancashire (now Merseyside), England, Parkinson began his career at Anfield rising through the youth ranks and breaking into the first team in 1903.

He made his debut on 3 October in a 2–1 victory against Small Heath at Muntz Street, scoring after sixteen minutes.

Injury hampered Parkinson's career to some extent, including a broken wrist sustained in a match against Woolwich Arsenal in Liverpool's championship-winning season of 1905–06.

Parkinson's most prolific season for the Reds was the 1909–10 campaign, which saw him top the league's goalscoring list with thirty goals in 31 games.

The 1913–14 season proved to be Parkinson's final for Liverpool, making only six appearances, his last being a 1–2 defeat at Burden Park against Bolton on 14 February 1914.