Hello Silke,
Please see the link below for a run down of some excellent ramen shops in Kyoto. Unfortunately, I don’t know of any ramen-ya in Arashiyama. Arashiyama is a real tourist destination and ramen is more the food that local residents eat. So, I suspect there aren’t much for red-hot ramen destinations there.
http://openkyoto.com/kyoto-support/topic/ramen-great-ramen-shops-in-kyoto
I checked Tabelog, which is a gourmet community site in Japan. I didn’t see anything too exciting in the Arashiyama area.
http://r.tabelog.com/RC110101/kyoto/A2604/?sk=らーめん
I think that you would want to try Sumashi Ramen at Takaraya (Ponto-cho location) and maybe Soy Milk Ramen at Mamezen Soba (but Mamezen is very often closed without notice).
Enjoy!