Soup up originated in the U.S. in the late 19th century, though it wasn't widely used until the 20th century. Its exact origins are unknown, but it could be short for supercharge, or it might come from a horse-racing slang term for injecting horses with narcotics meant to make them run faster.
Interesting. I never saw it spelled like that before. Looks like no one knows how it should be spelled, so all variations are fine.