You can compete in an archery contest. You can learn archery. But you cannot "do" archery. The only verb I know is "shoot": you shoot arrows at a target using a bow.

What is the verb for archery?

Arching. NSOED has "arch" as a verb meaning "engage in archery", dating from the mid 17th century.

What is the act of archery called?

Archery is the sport, practice, or skill of using a bow to shoot arrows. The word comes from the Latin arcus, meaning bow. ... A person who practices archery is typically called an archer or a bowman, and a person who is fond of or an expert at archery is sometimes called a toxophilite or a marksman.