As long as the U.S. Food and Drugs Administration has not fully approved the COVID-19 vaccine, the U.S. military troops have the option to take it or not. So far, the FDA has only issued emergency authorization, and it will take around two or three years more before they will fully approve it. Convincing the service members to take the vaccine voluntarily has become a challenge to Pentagon, especially as troops have kept their coronavirus cases relatively low.
Source: https://www.voanews.com/covid-19-pandemic/pentagon-wont-force-us-troops-take-covid-19-vaccine