A joke about a “joint” bank account has been cited in print since at least 2009:
 
“A Rastafarian walks into a bank with a huge bag of dagga wanting to open a joint account.”
 
     
Runner’s Talk—Forum
Joke of the Day (PG 13)
emmy   
October 27th, 2009, 5:18 am #1302
A Rastafarian walks into a bank with a huge bag of dagga wanting to open a joint account.
 
Twitter
Sandipan Sen
@sensandipan
RT @sickipedia: A Rastafarian walks into a bank and hands the cashier a bag full of marijuana. “Sir, what’s (cont) http://tl.gd/13f6pq
2:38 PM - 30 Apr 2010
       
Twitter
Mandela
@JuanTake
RT @Harrleyquinn23: A rastafarian dude walks into a bank n hands a cashier a bag full of weed. The angry cashier ... http://tmi.me/6l8oR
6:31 AM - 4 Feb 2011
   
Twitter
Paul Sundstrom
@Paul_Sundstrom
A Rastafarian walks into a bank with a bag of weed and says,” I’d like to open a JOINT account!!!”
10:18 AM - 26 Jun 2011
 
Facebook
Tony Richard Barker
January 26, 2014 ·
A Rastafarian walks into a bank and hands the cashier a bag full of marijuana.
Sir, what’s this for? says the surprised lady.
The Rasta replies, Me come to open a joint account..
 
Reddit—Jokes
A Rastafarian Gentlemen walks into a Bank
submitted March 24, 2017 by blakemon1
He hands a cashier a bag full of marijuana. The angry cashier asks ‘Sir what on earth is this…? The Rastafarian replies “wa yah ask foolish question mon, mi come to open a joint account”
   
Twitter
Vidya Birkhoff
@theartofvidya
A Rastafarian walks into a bank with a 5lb bag of weed, hands it over to the teller and says “Me here to open a joint account!
1:52 PM - 28 Oct 2017
 
Twitter
Neil Wellington
@wildwellie
A Rastafarian walks into a bank, with a bag full of marijuana.
He wanted to open a joint account. #1PUN
3:43 AM - 27 Jun 2018