At stake is a House seat Republicans have held for more than two decades. Trump easily won with 60 per cent of the votes cast in the 17-county congressional district of south-central Kansas during the November election.
Tuesday's special election will fill the vacancy created when Trump chose former US Republican Mike Pompeo as his CIA director.
The race in the heavily Republican district makes the state's GOP Treasurer Ron Estes the expected front-runner. But his Democratic opponent.