Your sentence is perfectly correct, Paul.
There are many different issues here, and each person has taken a different angle on the three-word phrase 'has tested positive':
<ul><li>@ Derek and @tempus.edax.rerum focused on the tense. As @tempus explained, it is correct to use a present perfect construction (has + past participle). One of the main uses of this tense is to refer to something which (a) happened at an unspecified recent time and which (b) has a direct impact on the present moment. When we tell someone some news, it is standard to use the present perfect: "Hey, have you heard? x has happened!"</li></ul>
<ul><li>@človek took exception to the voice; he felt it should be a passive construction: 'has been tested positive' rather than 'has tested positive'. I can understand @človek's discomfort, but the passive is actually wrong in this case. You might use a passive to refer to the fact of undergoing a test, as in "He has been tested already" or "He has been tested regularly". But this sentence is not about the fact of having undergone a test: it's about the result. When we talk about test results, we use the ergative form of the verb - the phrase 'to test positive' or 'to test negative': this is an active construction. If it still sounds wrong, think about the parallel phrase, "The pasta has cooked quickly" - another ergative verb where the standard object of the verb is used as its subject. Odd as it looks, the grammar is 100% correct.</li></ul>
<ul><li>For me, the odd thing about the sentence is the lack of preposition. You might have expected 'Mr Peters has tested as positive', perhaps. But no. As in the dictionary entry which @Michael quoted, 'test positive' is an accepted phrase meaning 'produce a specified result in a medical test'.</li></ul>
<ul><li>@Peter commented on the sad reality. Unfortunate indeed. What is even more unfortunate is that so many of these cases could have been prevented if certain politicians had made different choices. But let's not go there.......</li></ul>