“Scrounge” is the virtual twin of the last word I wrote about, “wangle.” Both mean roughly the same thing, emerged in Britain as World War I slang, and after a few decades got adopted in America.
The OED definition for “wangle” is “To accomplish (something) in an irregular way by scheming or contrivance; to bring about or obtain by indirect or insidious means (something not obtainable openly).” “Scrounge” is more specifically about getting; the dictionary defines it as “To seek to obtain by irregular means, as by stealth or begging; to hunt about or rummage.”
The OED cites a 1909 book, Passing English of the Victorian Era: Dictionary of Heterodox English, Slang, and Phrase, which defines “scrunging” as “(Country Boys’), stealing unripe apples and pears—probably from the noise made in masticating.” The word, with an added “o,” gained wide currency and a more general sense during the war. George Goodchild’s 1918 book Behind the Barrage provides this explanation:
In the category of “odd jobs” came “scrounging.” “Scrounging” is eloquent armyese — it covers pilfering, commandeering, “pinching,” and many other familiar terms. You may scrounge for rations, kit, pay, or leave. Signallers are experts at it, and they usually scrounge for wire. Scrounging for wire is legitimized by the War Office, and called by the gentler name “salving.”
As for U.S. adoption, here’s the Google Ngram Viewer graph for “wangle”:
And here’s the one for “scrounge”:
For whatever reason, “scrounge” reached parity later (in the 1960s as opposed to the 1940s), but ultimately became more (rather than equally) popular in the U.S. than in the U.K. Go figure!
notoneoffbritishisms.com 
Also, in “The Great Escape” the character played by James Garner, was called “the Scrounger”, after his ability to acquire what was needed for the escape committee.
Not sure what “The Great Escape” means in the US, and whether the choice of nickname came from a scriptwriter, or actual events.
from: https://en.wikipedia.org/wiki/The_Great_Escape_(film)
James Garner as Hendley “The Scrounger”
Although Garner was American, his character was in the RAF and it was a British made film about RAF POWs. Would that have had any influence in the US?
Garners character was a USAF officer (along with Steve McQueens). In reality US and UK forces were not held in the same camps, but the studios needed a US angle.
That said, maybe Hendleys nick name was for UK consumption /.
For whatever reason, “scrounge” reached parity later (in the 1960s as opposed to the 1940s), but ultimately became more (rather than equally) popular in the U.S. than in the U.K. Go figure!
My guess is that may be connected with James Garner’s role as Hendley “The Scrounger” in The Great Escape (film), one of the highest-grossing films of 1963 (#17 of 20). I didn’t know until today that he was a scrounger in real life as well: “James Garner had been a soldier in the Korean War and was twice wounded. He was a scrounger during that time, as is his character Flt Lt Hendley.” https://en.wikipedia.org/wiki/The_Great_Escape_(film)#Casting
Perhaps that aspect received US publicity at the time?
(I’m a Brit and saw the film in England initially, but I’ve been a US resident for 22 years.)
Regards,
Bruce
In the UK, “scroungers” is the favourite term in the tabloid press to describe people living off benefits, the implication being that they are living off benefits rather than finding gainful employment.
The term I know for stealing apples is scrumping. And scrumpy is very strong cider.
There’s a line in “5:15” from Quadrephenia by The Who …
“On a raft in the quarry
Slowly sinking
Back of a lorry
Holy hitching
Dreadfully sorry
–>Apple scrumping
Born in the war
Birthday punching”
In my family, we use scrounge almost entirely to mean ‘to find food in the house to eat as opposed to going out for food or cooking a fresh meal’ as in: “What are we doing for supper?” “We’re scrounging tonight.” This sense is clearly extended from the other but dictionaries lack this specific definition, so I’m wondering if it’s isolated to my family or region (southern US).
Here’s another song lyric, this one using ‘to wangle’ – illustrating its meaning is different from ‘to scrounge’. It’s the start of the second verse of Suspended in Gaffa by Kate Bush:
He’s gonna wangle
A way to get out of it.
She’s an excuse
And a witness who’ll talk when he’s called.