That is racist and not funny in the least bit. Not because of the drinking, but because of the over exaggerated Irish accent, that in the context which you state it, makes all Irish people sound stupid.
I got one.
An Irish man moves to Boston from Dublin leaving his family behind in Ireland.
Every night he goes to a bar in Boston and orders beers four at a time. He never talks to anybody, just orders his four beers at a time. The bartender finds this rather odd, and asks the Irish man why he is doing this.
The Irish man replies by saying that he left his three brothers back in Ireland, and when he left, he'd promise that he'd drink a beer for them everytime he had a beer. Hence the four beers at a time.
One day in early March, the Irish man comes into the bar and only orders three beers. The bartender thinks that this is rather odd, but does not say anything about it to the Irish man. This goes on for about two weeks, and finally one night the bartender approaches the irish man sympathetically.
"I'm sorry to hear about your loss", the bartender says. The Irish man, looking confused, says "My Loss?". The bartender is embaressed and says "Well i just thought that one of your brothers had died". The Irish man turns to him and says, "No, those a$$holes are fine, I gave up beer for lent".