Police and crime commissioner Tony Hogg's decision came after the launch of consultation on Monday.
A spokesman said reaction on social media showed "probably two thirds" of people were against a rise.
"We got a very good idea of what people were thinking, so in a way social media has done the job for us."
Mr Hogg had been planning to hold a referendum next May on adding about Â£25 a year to the bill of the average band D property in Devon and Cornwall.
He said the rise in the police share of council tax could save 350 officers.
It came amid a projected budget cut of Â£39m next year, with the loss of up to 760 police officers and all 360 community support officers.
Reaction to a council tax rise on Facebook pages, including that of BBC Spotlight, included comments such as: "Why should we be asked to pay more for our policing? We are paying a fortune in council tax as it is this will just end up in the pockets of those at the top."
Other reactions included: "Council Tax is already too high" and "I'm against this proposal because it will let the Government off the hook".
In May, Bedfordshire council tax payers rejected a planned rise in council tax for the police.
Mr Hogg's decision came after the government admitted it had made a "statistical error" in a new formula which assesses population size and other data to calculate funding.
He is now waiting for an announcement from Chancellor George Osborne, expected later this month, on what funding the force will get.
Plans for a referendum on raising council tax for Devon and Cornwall Police have been dropped after a backlash on social media.