Possibly. Maybe probably if you consider a long time frame. There is no indication immunity from an infection lasts a long time. There isn't even any indication immunity from a vaccine will last a long time. There are a few patients who have been reported becoming reinfected, and they had a worse time the second time around. Some other docs are skeptical, wondering if the first diagnosis might have been incorrect especially given the inaccuracy of testing. But from what I have heard from interviews with the docs who had the patients infected twice, they were there and this is what they saw. But it's a tiny number of people so far. The answer to your question is, I believe, currently, nobody knows a lot about this yet but probably you can but most likely won't.
There have been 25 cases of reinfection, according to this group that's been tracking it - https://bnonews.com/index.php/2020/08/covid-19-reinfection-tracker/
The average interval between infections is 78 days (and there's only 25 confirmed cases so far), but there is a wide range. There are 579 suspected cases.
The shortest is 12 days - the details say it was not really a reinfection, but a co-infection of two virus variants, though there is one at 13 days of an actual reinfection, a healthcare worker. The longest is 185 days.