Cllr Steve Siddons, who leads the Labour Group on the council, also said the authority should look once more at developing a multiplex in the town centre.
His comments came after the director of Benchmark Leisure, Roland Duce, told Yorkshire Coast Radio that its proposed cinema, apartments and car park development on the former Atlantis waterpark site would not open for “maybe another 20 months”.
Benchmark’s scheme has been beset by a number of delays and planning issues, having originally been scheduled to open in 2018.
The most recent plans lodged with Scarborough Council reduced parking spaces, from around 300 to 109 and increased the number of apartments from 24 to 63.
Cllr Siddons has now called on the council to go back to the drawing board.
He told the Local Democracy Reporting Service: “Isn’t it time to completely review the location of the new cinema for the town?
“When the plans were first released, Labour insisted the cinema should be built in the town centre in accordance with planning rules.
“The Conservatives chose to ignore those rules and look where that has left us, with no new cinema at all in the foreseeable future.
“They have propped up the North Bay developer for so long. It’s time to revisit the plans to give Scarborough a new cinema.”
The current application, which now includes a gym on the site as well as the six-screen cinema and restaurants, has garnered a number of objections.
The Environment Agency has objected due to concerns over flooding and Yorkshire Water has also objected as it has worries over drainage from the site.
The Yorkshire Coast and Ryedale Disability Forum has lodged an objection as has a member of the public querying why there are only 31 residential car parking spaces for 63 apartments.
Carl Gavaghan, Local Democracy Reporting Service