Community safety minister Ash Denham said there is "no barrier to accessing testing", though officers will first have to contact Police Scotland's HR department for them to determine if checking them is "appropriate".
Tory MSP Alexander Stewart pressed her on the issue in Holyrood, saying "unfortunately some officers report being spat at and coughed at in a disgusting attempt to spread coronavirus".
Ms Denham said when officers have such a Covid-19 "interaction" the force can "offer facilities for an assessment and where appropriate a test".
The minister confirmed they "do not have to be symptomatic in order to access that testing".
In a statement released tonight, Deputy Chief Constable Fiona Taylor said: "Police officers and staff are playing a vital role in the work to protect the NHS and save lives, but assault is not simply part of that job. Therefore, it's important that we do everything we can to protect our people and I'm delighted that the Scottish Government has agreed to our request that officers and staff can have access to tests in these circumstances."
Earlier this week, Police Scotland revealed that more than 100 coronavirus-related attacks on officers and staff had now been recorded.
Ms Denham added: "The police are at the front-lines of this, they are out there putting themselves at risk on a daily basis in order to keep the rest of us safe.
"We want them to have confidence that if they are concerned they can get access to testing, we would expect them to be able to do that."
"Any police officer or member of staff who is concerned about their health or their well-being following an assault of any kind to do with the Covid-19 situation, what they need to do is contact Police Scotland's HR department to be risk assessed and following that a decision would be made on whether testing is appropriate for that individual."