From Grammarphobia and the Oxford English Dictionary:
The word “route” can be pronounced either ROOT or ROWT in the US.
This is true for both the noun, meaning a course or path, or the verb, meaning to send something by a specific course or path.
In Britain, though, only the first pronunciation is common for the noun and verb. But the British once had both versions too.
As the Oxford English Dictionary explains, the second (ROWT) disappeared from standard British English sometime during the 19th century, “but is still widespread in North America.”
The noun “route” is very old, and was probably first recorded around 1225, the OED says.