Yes - Barsel - they can :
"Because it’s possible to get reinfected and COVID-19 can cause severe medical complications, the CDC recommends that people who have already had COVID-19 get a COVID-19 vaccine.
In addition, COVID-19 vaccination might offer better protection than getting sick with COVID-19. A recent study showed that unvaccinated people who already had COVID-19 are more than twice as likely as fully vaccinated people to get reinfected with COVID-19.
Recent research also suggests that people who got COVID-19 in 2020 and then received mRNA vaccines produce very high levels of antibodies that are likely effective against current and, possibly, future variants. Some scientists call this hybrid immunity. Further research is needed.
If you were treated for COVID-19 with monoclonal antibodies or convalescent plasma, wait 90 days before getting a COVID-19 vaccine."