Yes. The following is from the Centers for Disease Control and Prevention website focusing on COVID-19 vaccines:
COVID-19 vaccines are safe and effective. Millions of people in the United States have received COVID-19 vaccines, and these vaccines have undergone the most intensive safety monitoring in U.S. history. This monitoring includes using both established and new safety monitoring systems to make sure that COVID-19 vaccines are safe.
Results from these monitoring efforts are reassuring. While some people don’t have any side effects after getting a COVID-19 vaccine, many people will have mild side effects after COVID-19 vaccination, like pain or swelling at the injection site, a headache, chills or fever. These reactions are normal and show the vaccine is working. A small number of people have had a severe allergic reaction (called “anaphylaxis”) after vaccination, but this is extremely rare and when it does happen, vaccination providers have medicines available that they can use to effectively and immediately treat the reaction. You will be asked to stay for 15 to 30 minutes after you get your vaccine so you can be observed and provided treatment in the rare case it is needed.
The combination of COVID-19 vaccination and following the CDC’s recommendations to protect yourself and others offers the best protection from COVID-19. The CDC recommends you get a COVID-19 vaccine as soon as you are eligible.