The English verb phrase 'to tie one on' is used as an idiom to mean 'get drunk to an unusual or excessive degree'. According to the Google Ngram Viewer, the phrase first gained currency in published works at about the time of World War II and has increased steadily in frequency since then, with a significant dip in the 1960s and a leveling off since 1980 or so. (Note that these results include all appearances of the phrase, including an non-idiomatic uses.)

Curious minds must be in a fever over how and when this usage began. What is this 'one' thing is that gets tied on, what does it get tied on to, and what on earth does any of this have to do with binge drinking?

Well, the answer is sadly disappointing. It seems that no one actually knows. The Oxford English Dictionary tells us that the first known use in print was in a book called "Western Folklore", which was printed in 1951, and compares it the British phrase 'tie a bun on' from the turn of the century (not this one, but the one before last). That's little help, though, because no one knows what that has to do with getting drunk either.

How is it that such phrases that have no obvious relation to their meanings can come into wide use without anyone knowing their origin? The truth must be out there.