William Henry Thompson (March 10, 1848 – August 12, 1918) was an American archer who competed in the early twentieth century.
He won two bronze medals in Archery at the 1904 Summer Olympics in Missouri in the double York round, when Robert Williams won silver and his second bronze in the double American round.
In the team competition he won the gold medal.
He was born in Calhoun, Georgia and died in Seattle, Washington.