They take on Bradford side Westwood Park at Askern Miners Welfare in the second round on Sunday (1pm).
Entry is £2 on the gate. Children and concessions will be admitted for free.
Scawthorpe beat Newark-based outfit RHP Sports and Social 4-0 in the first round in December.
They qualified for England’s most prestigious Sunday League competition after winning the Doncaster Rovers Sunday League Premier Division title last season.
The FA Sunday Cup was founded in 1964. Scawthorpe are the only club from South Yorkshire in this season’s competition and are understood to be the first Doncaster club to ever compete in it.