Though becoming more popular as a folk-prophylactic, there is no evidence that tonic water can treat or prevent becoming infected with SARS-Cov-2.
One liter of tonic water contains a small amount of quinine (~83mg). Synthetic versions of quinine are hydroxychloroquine and chloroquine. These synthetic versions are used to treat malaria at (~400mg/day) and recently, they have been used in COVID-19 trials (5mg/kg/day). To be effective then, one would need to drink between 4 to 5 liters of tonic water to match a comparative medicinal quinine dose. The problem, of course, is that natural quinine itself has not been tested on COVID-19 patients. The synthetics are being tested and there aren't any scientific results at this time. Early reports from ICU doctors are that the drugs don't appear to be doing anything for critically-ill patients. Patients believe so, but this isn't scientific. This is akin to how some believe that a rabbit's foot brings them luck. It probably doesn't, but if they believe it does, any positive event in their lives will then be attached to the rabbit's foot. We see this in all unscientific beliefs.