Three had tested positive for Covid-19 over the last few weeks.
Care UK, which runs Millers Grange on Curbridge Road, said the fourth residents was also displaying symptoms of coronavirus, but hadn't been tested.
One of the three who tested positive had been transferred to hospital recently.
All staff at Millers Grange have been provided with all 'of the appropriate PPE and have been using it meticulously', according to the Regional Director for Care UK.
Daniel Turner-Naylor added: "We are deeply saddened by these deaths and send our condolences to the friends and family of these residents.
"Since the first cases of coronavirus in this country, our teams have been carefully following a pandemic plan which is based directly on guidance from Public Health England and the NHS.
"I can't thank the team enough for their dedication to following this plan and for continuing to deliver highly professional and compassionate care in this incredibly challenging time."
The news comes as fears grow that hundreds of people are dying with coronavirus in care homes but not being included in daily government updates.
Britain's biggest care home operator, C-One, revealed two-thirds of its homes have been affected and more than 300 people have died in them.
Meanwhile, Care England said there have been thousands of cases and deaths in the homes it represents.
Tests have now been pledged to all who need them in care homes - including staff and residents - with the Care Quality Commission charged with coordinating who will get them and when.
Currently the government's daily deaths update only includes patients who die after testing positive for the virus in hospital.