Other forms: inducted; inducting; inducts
Induct is what groups do when they formally accept new members, like the honor societies that, every school year, induct students who meet the qualifications.
When you induct someone into a group, you formally welcome him or her as a member. The word is typically used to describe official acceptance of a position or admittance into an organization, such as a professional society. It can also be used to describe someone who has formally enrolled in the military. Don't use it for informal joining, though — you wouldn't induct a new friend or be inducted at the gym where you have just started a membership.