The National Care Forum said the target will be a significant challenge for health services across England, but achieving it would be the "booster" that everyone needs.
There were 7,017 care home residents in Lincolnshire as of December, according to analysis of Care Quality Commission data by CSI Market Intelligence.
GPs and local vaccination services have been asked to give injections to every care home resident in their area by the end of January.
With the rollout of the Oxford-AstraZeneca vaccine on January 4, this is a target of around 251 per day in Lincolnshire.
The CSI-MI figures assume an 85% occupancy level in the area, which is the national average, but there could be as many as 8,255 residents in Lincolnshire if all available beds are in use.
There are around 389,000 care home residents in England who, along with their carers, make up the Joint Committee on Vaccination and Immunisation's first priority group for jabs.
Vic Rayner, executive director of the NCF, said: "The scale of the challenge set by government over the next month is significant.
"It will rely on huge amounts of local communication and coordination between care homes, GPs and local public health teams.
"The response to the vaccine so far has been incredible, with residents and staff embracing it when available.
"Everyone is seeing this as a way forward for this most vulnerable population and being able to mark it as ‘job done’ by the end of the month will literally be the booster that everyone across the country needs."
With England in another lockdown, Prime Minister Boris Johnson has set a target for the four highest priority groups to be vaccinated by mid-February.
Care home staff are all covered in the top two groups, with almost one million of them across England, according to CSI-MI's analysis of Skills for Care data.
The data shows there were around 16,225 employees in Lincolnshire as of September 2019.
Age UK said the rollout of the Oxford vaccine was good news as it is much easier to transport.
Charity director Caroline Abrahams said: "Care homes have had a torrid time since the start of the pandemic and it is vital that vaccinations happen as quickly and efficiently as possible and that residents and the care staff get the protection they need."
But she added that the country needs to control the spread of the new, highly infectious Covid-19 variant, and protect as many people as possible.
Health Secretary Matt Hancock said: "The NHS is doing everything it can to vaccinate those most at risk as quickly as possible and we will rapidly accelerate our vaccination programme.
"While the most vulnerable are immunised, I urge everybody to continue following the restrictions so we can keep cases down and protect our loved ones."
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