From Proto-Germanic *rattaz (“rat”), from Proto-Indo-European *rēd- (“to scrape, gnaw, scratch”). Akin to Old Saxon ratta (Middle Low German ratte), Dutch rat (“rat”), Old High German ratta, rato (whence German Ratte, Ratz), Old Norse rotta (whence Icelandic rotta, Danish rotte, Swedish råtta, Middle Low German rotta (“rat”), Irish radan (“rat”), Latin rodere (“to gnaw”). More at rodent.
The Germanic form rat-, ratt- is common in Germanic languages, and in Romance languages through Vulgar Latin *rattus which was borrowed into the Romance languages from a Germanic source (as evidenced by regular sound correspondences of Proto-Indo-European e, ē → Germanic a, and Proto-Indo-European d to Germanic t. The Italic cognate of the Proto-Indo-European word was Latin rodens, rodent- from rodere). Compare French rat, Spanish rata, Italian ratto.