Wordorigins.org

This is a rather etymologically mysterious term to most people today, but an examination of the changes in meaning of drag over the centuries makes it clear why we call racing for fastest acceleration drag racing.

In the 16th century, drag was a term for a sledge, a platform with skids, not wheels, that could be dragged behind a horse or ox. From an act of Elizabeth I of 1576:

Sleades, carres, or drags, furnished for...repairing...high wayes.¹