It's not something I've ever specifically seen, it seems to be more branch specific. In theory, each branch is likely to have its own unique 'anthem', shall we say.
The Royal Armored Corps has "My Boy Willie", but the lyrics are different to the traditional.
Example: Original song first two verses
Oh where have you been all the day
My boy Willie?
Oh where have you been all the day?
Oh Willie won't you tell me now?
I've been all the day courting of a lady gay
But she is too young to be taken from her mother.
Oh can she brew and can she bake
My boy Willie?
Oh can she brew and can she bake?
Oh Willie won't you tell me now?
She can brew and she can bake
She can make a wedding cake
But she is too young to be taken from her mother.
Compared to the Royal Armored Corps
The Amoured Corps to the fore,
My boy Willie,
The Armoured Corps, the King or War,
Willie is the fighting breed,
Day or night, dark or light,
The foe will know we're there all right,
We'll be fighting in the front to our battle cry,
The Armored Corps' tanks are there,
My boy Willie,
With clanking treads, and our steel bare,
Turrets in line, and hull combine,
The grandest warriors of our time,
We'll be fighting in the front to our battle cry,
The US Army officially has an armor song.
The Army is a team that tackles any job that's tough,
But when the land is rugged and the enemy is rough,
Who do they call to make them say "I quit, I've had enough!"?
Nobody but the ever rolling,
Hit them again and keep it rolling,
Nobody but the ever rolling ARMOR!
19 years wearing Armor Brass, I have never once heard it. That's it, by the way, all six lines. Bear in mind, though, that Armor was not an official branch in WW2 (Officially created post-war), so the anthem post-dates that.
You are more likely to hear Garryowen, the Cavalry song. If you've ever watched an old west movie with cavalry, you know the tune. And, of course, Cavalry did exist in WW2.
First verse and chorus:
Let Bacchus’s sons be not dismayed,
but join with me each jovial blade,
come booze and sing and lend your aid,
to help me with the chorus:
Instead of spa we’ll drink down ale
and pay the reckoning on the nail,
for debt no man shall go to jail
from Garryowen in glory.
Unfortunately, it seems almost nobody knows the words to this one either, they just clap and stomp. Daft. As an aside, Garryowen is often written as a person's name, Gary Owen, which is wrong. Gearraieobhainn (pronounced, oddly, garryowen) is a town in Ireland, now a suburb of Limerick.
A lesser-known tune, though not unlikely sung by a certain demographic in the US Cavalry would have been "Jine the Cavalry",
We're the boys that rode around McClennanian,
Rode around McClellanian, Rode around McClellanian.
We're the boys that rode around McClellanian,
Bully boys, hey! Bully boys, ho!
If you want to have a good time, jine the cavalry!
Jine the cavalry! Jine the cavalry!
If you want to catch the Devil, if you want to have fun,
If you want to smell Hell, jine the cavalry!
There was a Tank Destroyer Men song, which would have been only WW2 as that was the only time the TDs were around. Reminds me a lot of a Tom Lehrer rendition for some reason.
We're proud to tell the world that we are Tank Destroyer Men,
We're off to fight the enemy but we'll be back again
We come from almost every State in the good old USA
We're raring to go and meet the foe so we'll be on our way....
The Germans have* The Panzerlied, the Armor Song (Or Tank Song). New lyrics to an old sailor's tune.
This one is much more well known. First verse follows.
Ob's stürmt oder schneit,
Ob die Sonne uns lacht,
Der Tag glühend heiß,
Oder eiskalt die Nacht,
Bestaubt sind die Gesichter,
Doch froh ist unser Sinn,
Ist unser Sinn;
Es braust unser Panzer,
Im Sturmwind dahin
(Translation) Whether it storms or snows,
Whether the sun smiles upon us,
[Whether in] The day's scorching heat,
Or the ice-cold of the night,
Dusty are the faces,
But joyous is our mind,
Yes, our mind.
Our tanks roar there,
There in the stormwinds.
However, they aren't anything that you would specifically sing in the tank just randomly to keep happy. Normally, at least. One would presume that the tank crews would sing whatever was generally popular at the time, much like everyone else.
*I use the present since, as far as I know, all the German tank crews still know and sing it. The German minister of defense rather (in)famously prohibited the German Army from publishing it in song books in 2017 as a denazification move, the song was adopted in 1933, but traditions die hard, the lyrics have nothing to do with nazism, and it is an internationally known tune. Chile, for example, has been known to play it in military parades when ex-Bundeswehr Leopards and Marders roll by.