late Old English ræt "rat," of uncertain origin. Similar words are found in Celtic (Gaelic radan), Romanic (Italian ratto, Spanish rata, French rat) and Germanic (Old Saxon ratta; Dutch rat; German Ratte, dialectal Ratz; Swedish råtta, Danish rotte) languages, but connection is uncertain and origin unknown. In all this it is very much like cat.
Perhaps from Vulgar Latin *rattus, but Weekley thinks this is of Germanic origin, "the animal having come from the East with the race-migrations" and the word passing thence to the Romanic languages. American Heritage and Tucker connect Old English ræt to Latin rodere and thus PIE *red- "to scrape, scratch, gnaw," source of rodent (q.v.). Klein says there is no such connection and suggests a possible cognate in Greek rhine "file, rasp." Weekley connects them with a question mark and Barnhart writes, "the relationship to each other of the Germanic, Romance, and Celtic words for rat is uncertain." OED says "probable" the rat word spread from Germanic to Romanic, but takes no position on ultimate origin.
Middle English common form was ratton, from augmented Old French form raton. Sense of "one who abandons his associates" (1620s) is from belief that rats leave a ship about to sink or a house about to fall and led to meaning "traitor, informant" (1902; verb 1910). Interjection rats is American English, 1886. To smell a rat is 1540s; "to be put on the watch by suspicion as the cat by the scent of a rat; to suspect danger" [Johnson]. _____-rat, "person who frequents _____" (in earliest reference dock-rat) is from 1864.