“Tie one on” (to get drunk)

To “tie one on” means to become drunk. A March 1933 newspaper article on American slang defined it, “tie one on, to become intoxicated.” It’s not explained what is being tied on to what.
 
Newspaper cartoons often showed a drunk with an ice pack wrapped around the head (like a ring). It’s possible that this is what was “tied on” to an intoxicated person.
 
   
The Free Dictionary
tie one on and hang one on; lay one on; tie it on
Sl. to get drunk
 
(Oxford English Dictionary)
to tie one on slang (chiefly U.S.): to get drunk.
1951 Western Folklore 10 82   The Act of Drinking:..to swill one down; to tie one on.
1962 J. Onslow Bowler-hatted Cowboy xix. 186   You used to tie one on with the boys.
1982 A. Mather Impetuous Masquerade vii. 107   He had..tied one on, if you know what I mean.
 
24 March 1933, The Morning Oregonian (Portland, OR), “Phoney Lingo Cops Weasel and Wooky,” pg. 1, col. 5:
“Are you a wooky, or have you tied one on?”
Pg. 2, cols. 4-5:
Witch kitty, a difficult final exam; weasel, a bright student; wooky, mental unbalance; tie one on, to become intoxicated; cop a phinney, steal another man’s girl.

3 April 1942, The Times-Picayune (New Orleans, LA), “Biologists Hear of ‘Jag” Cure in Boston Meeting,” pg. 39, col. 4:
The dogs really “tied one on.”
 
They were given shots of straight alcohol ...
 
25 September 1944, Cleveland (OH) Plain Dealer, pg. 5, col. 7 ad:
And are you ever missing a simply knockout Junior Miss black day ‘n’ date dress with a separate jeweled peplum you tie-on “to tie one on” after office hours.
(The Lindner Coy—ed.)
 
23 May 1947, Evening World-Herald (Omaha, NE),  “It Happened Last Night” by Earl Wilson, pg. 9, col. 1:
FDR liked a cocktail. Pegler used to tie one on—worst thing I can think of against whisky.
 
Google News Archive.‎
30 December 1955, Nashua (NH) Telegraph, “Around the Town,” pg. 6, col. 5:
If you are going to drink then for heaven’s sake get someone to drive your car. (...) But when you tie one on, as they say, you endanger other lives than your own—especially when you are behind the wheel of a car—and if you don’t care about your own life the police care that you aren’t a menace to others.
 
Google Books
The Un-Americans
By Alvah Cecil Bessie
New York, NY: Cameron Associates
1957
Pg. 147:
“An old Spanish custom,” said Lang. “We tie one on. We paint the town. We make a night of it.”
 
Google Books
Teenagers:
A national dilemma; how we can shape tomorrow’s leaders
By Johnnie W. Cason
New York, NY: Exposition Press
1961
Pg. 47:
Girls haven’t much control over whether boys tie one on or not, although a boy will get a kick out of letting a girl feel noble about reforming him when he doesn’t much care for drinking anyway.
   
OCLC WorldCat record
I’m gonna tie one on tonight
Author: Wilburn Brothers.
Publisher: New York : Decca, [1965]
Edition/Format:   Music LP : Country music : English
 
Google Books
The Sterile Cuckoo
By John Treadwell Nichols
New York, NY: D. McKay Co.
1965
Pg. 178:
“If you bring him a drink he’ll tie one on,” Pookie said, grinning salaciously.
 
Google Books
A Bad Man
By Stanley Elkin
New York, NY: Random House
1967
Pg. 301:
‘Do you want to go out?’
‘What’s there to do?’
‘There’s this movie downtown.’
‘A movie? You think?’
‘We could go tie one on.’
‘Well, tomorrow there’s work.’
 
Google Books
The Synonym Finder
By J. I. Rodale, et al.
Emmaus, PA: Rodale Press
1978
Pg. 262:
tie one on, SI. go on a binge or bender or toot, ...