Originally from York, Western Australia, where he played in the local league, Screaigh made his debut for East Perth in 1932, and went on to win three club best-and-fairest awards in his first three seasons.

Playing mainly as a rover, Screaigh was a member of East Perth's 1936 premiership side, and also led the club's goalkicking in three seasons.

He first attracted the attention of East Fremantle recruiters at the end of the 1930 season, but declined their invitation after no job could be found for him in Perth.

[7] He won his third consecutive best and fairest award, and was also East Perth's leading goalkicker, in part due to the absence of a key marking forward.

The club subsequently won the grand final against Claremont 11.5 (71) to 9.6 (60), with Screaigh again kicking a goal with the last kick after the match[8] After the retirement of previous captain Mick Cronin due to a leg injury before the 1940 season, Screaigh was appointed captain of the club for the 1940 season, with Cronin remaining in a role as non-playing coach.

Screaigh had married Jean Augustine Marwick on 3 December 1932 at St Patricks Catholic Church in York, with whom he had two daughters, Maureen (later Otto) and Deanne (later Hetherington).

Screaigh was one of the smallest players in the WANFL at the time, standing only 165 centimetres (5 ft 5 in) and weighing 61 kilograms (134 lb).

[25] He had only been recruited to East Perth after convincing the club secretary, F. D. Book, who had on appearances thought Screaigh was "too small and meek", to allow him to play in several scratch matches before the 1932 season.

Against Subiaco in July 1933, he kicked nine goals, at the time the second-highest goal-kicking total of a player playing as a rover in the league.