From the CDC:
"Yes, you should be vaccinated regardless of whether you already had COVID-19 because:
* Research has not yet shown how long you are protected from getting COVID-19 again after you recover from COVID-19.
* Vaccination helps protect you even if you’ve already had COVID-19.
Evidence is emerging that people get better protection by being fully vaccinated compared with having had COVID-19. One study showed that unvaccinated people who already had COVID-19 are more than 2 times as likely than fully vaccinated people to get COVID-19 again."