There is such a word router in fact from Merriam-Webster Online dictionary.
http://www.m-w.com/dictionary/router And it's 'rau ter' as you can see.
However, since this is a made-up word in computers, I would pronounce it as 'route ter' because it is routing after all. Some people may pronounce it as 'rau ter' - I have to admit that was my first reaction when I saw that word as well without knowing with a router is! Now if you look at the word -
Rout (a crowd of ppl) - the correct pronunciation is RAUT (from Merriam-Webster
http://www.m-w.com/cgi-bin/dictionary?va=rout)
So it's not surprising that ppl would say 'Rauter' and 'Router'. My personal take is that both are acceptable in the field of computers at long both parties know what each is talking about!
Hope that made sense.
2007-06-19 16:38:50 補充:
Keep in mind that Rout is still pronounce RAUT whether it's British or American english.