In a number of English dialects, the past participle, drunken, is not unusual and has been in use for at least two hundred years. From The English Dialect Dictionary, printed in 1900
1. Present tense:
(1) Dhrink, (2) Dreyngk, (3) Drunk, (4) Drynk
(1) Drak, (2) Drenk, (3) Drenked, (4) Drinked, (5) Dronk, (6) druck, (7) drunk.
3. Pp. :
(1) Dhrunken, (2) Drank, (3) Drinked, (4) Dronken, (5) Drucken, (6) Druckin, (7) Druken, (8) Drukken, (9) Drunk, (10) Drunken.
[…] e.Yks. Ah've drunken it, Wray Nestleton (1870) 303. 34. w.Yks. I'm dhry, I've drunken all my tea up F.P.T. s.Chs 1
e.Yks.= East Riding of Yorkshire—A Glossary of Words used in Holderness in the East Riding of Yorkshire. 1877
w.Yks = West Riding of Yorkshire—A Glossary of the Dialect of Almondbury and Huddersfield. 1883
s.Chs 1= Cheshire—The Folk-Speech of South Cheshire. 1887
From a prescriptive grammar called A Modern English Grammar on Historical Principles, Volume 6, first printed in 1954, come the following recommendations and historical notes [emphasis in bold, mine]
drunken. According to Fowler MEU the PE rule is that in adjunctal position only drunken is possible, whether expressing a permanent quality ‘given to drink’ or a temporary state ‘intoxicated’, while in the predicative a distinction is made between drunken ‘given to drink’ and drunk ‘intoxicated’: he was drunken and dissolute | he was drunk yesterday. Quotations: [...] McKenna M 283 a drunken man should never be so drunk as to not to know that he was drunk.—This rule was not was not strictly observed in former times: She has drunken = ‘intoxicated’ in the predicative: Ven 984 who is but drunken | Ant V. 2.219 Antony shall be brought drunken forth; […] In pure verbal function the en-form is archaic: Hewlett F 46 Sir, have you well-eaten and drunken? | Masefield C 312 She had drunken some drug to make her eyes bright. Thackeray […] N 20 Wherefore should the butler brew strong ale to be drunken three years hence. 
The authors also note other -en forms, rarely used in the ‘verbal function’; shrunken, stricken, cloven, carven, (en)graven, paven, proven, riven, shaven, clothen, writhen, wreathen, cursen, waxen, washen,
From a 2016 novel, by an American author
I don't think the chief gave him back the booze because he seemed normal after that and I didn't smell it on him. He probably just figured that he'd drunken it all anyway.
Masters, Mates and Mishaps
From a 2015 biography of James Dean
"The thing is, the journey doesn't stop. And, as the days go on, it gets better and it gets better and it gets better. Jim, James, you brought me here. But what's keeping me around is you guys ... You've shown me around. I've eaten hamburgers. I've drunken buckets of Coke."
Too Fast to Live, Too Young to Die - James Dean's Final Hours: ... (2015)
On the Internet; 29 DEC 2015, The Daily Mirror reporting on the death of Ian ‘Lemmy’ Kilmister, frontman of the heavy metal band, Motorhead.
He was arrested at the Canadian border for drug possession, yet his appetite for drugs and alcohol remained a constant throughout most of his career. He famously claimed he had drunken a bottle of Jack Daniel’s every day since turning 30, and he was also a proponent of amphetamines.
It was later rescheduled, but on his 100th birthday, on December 18, 2005, surrounded by friends and family, Vaughan had champagne. It was the first time he had drunken alcohol in his life—as a youth he had promised his mother he wouldn’t drink until he was 100. Several days later he died. source
An extract written by the 20th century Scottish author Neil Gunn
I dare say he's drunken every penny they've ever had.
An she's been there a the time? Hector was polite, but insistent. He wanted to know, but he didna want to press.
Fa else wid hae her? The driver waved an they stepped back
The Anarchy of Light: Neil Gunn: A Celebration (1991)
A poem by the 19th century Scottish author, John Knox
The Lovely Lady
For this, Lovely Lady! I may not complain,
Nor dim your fair image by breathings of pains,
A sigh may escape to the winds of the waste
But on you I think as of one of the blessed:
For eyes beaming sweetness and bland beauty bright,
Should waken no musings unless of delight—
I've drunken delight from your form passing by
Majestic, but mild, as the dawn on the sky.
The Twa Hares, and Other Pieces (1846) Dundee, Scotland.
In a 2014 translation of the Brothers Grimm's fairy tale, the unconventional and dialectal version was preferred:
“I've drunken and eaten for you,” the little man said, “and now I'll give you the ship. I'm giving you all this because you were so kind and took pity on me.”
The Simpleton from The Original Folk and Fairy Tales of the Brothers Grimm (first printed in 1812)
Last but not least, Morning Songs in the Night, Canada (1896)
I've sailed the dancing waters,
I've trod the golden strand,
I've spoke the sons and daughters
Of that enchanted land ;
I've drunken of her fountains,
The sweetest and the best ;
I've rambled o'er her mountains,
I've revelled in her rest