Republicans have scored an upset victory in a House race that started as a contest to replace Rep. Anthony Weiner after he resigned in a sexting scandal but became a referendum on President Barack Obama's economic policies.

Retired media executive and political novice Bob Turner defeated Democratic state assemblyman David Weprin on Tuesday in the special election to fill the New York seat vacated by Weiner, a seven-term Democrat who resigned in June.

With more than 80 per cent of precincts reporting, Turner had 54 per cent of the vote to Weprin's 46 per cent in unofficial results.

"We've been asked by the people of this district to send a message to Washington," Turner told supporters after the landmark win. "I hope they hear it loud and clear. We've been told this is a referendum. Mr. President, we are on the wrong track. We have had it with an irresponsible fiscal policy which endangers the entire economy."

Weprin did not immediately concede.

The heavily Democratic district, which spans parts of Queens and Brooklyn, had never sent a Republican to the House. But frustration with the continued weak national economy gave Republicans the edge.

Turner has vowed to bring business practicality to Washington and push back on spending and taxes.

The race was supposed to be an easy win for Democrats, who have a 3-1 ratio registration advantage in the district.

The House seat opened up when Weiner was pushed by party leaders to resign after sending sexually provocative tweets and text messages to women he met online.

The trouble for Weiner, who served seven terms, began when a photo of a man's crotch surfaced on his Twitter feed. He initially denied the photo was of him but later admitted it was. 

Weiner, who's married, resigned June 16 after two weeks of fighting off pressure to step aside. He apologized for "the embarrassment that I have caused" and said he hoped to continue to fight for the causes dear to his constituents.