Green’s Dictionary of Slang

(Irish) drunk.

1922		Joyce Ulysses 600: For instance, there was the case of O’Callaghan [...] among whose other gay doings when rotto and making himself a nuisance to everybody all round he was in the habit of ostentatiously sporting a suit of brown paper (a fact).
1939		(con. 1880–90s) S. O’Casey I Knock at the Door 55: The both of us were rotto.
1950		S. Murphy Stone Mad (1966) 9: He staggered in with the gallons empty and he rotto.