I learned it back in the '70s, but think I’ve forgotten some parts. I can’t find it on the Internet either. 
Oddfish. I’m very much into parodies, even have a few of my own published online. But I have never heard of this.
Is it possible you heard it on a local radio station done by local DJ’s therefore it did not have national exposure and thus you will never find it.
Do you mean “Star Trekkin” by the Firm?
No, I’m familiar with that one.
The one I’m thinking of starts out (to the best of my recollection)
It was Star Date 3416.9, and we’d swung the phasers 'round,
I said “Scotty, this here’s Captain Kirk, and I’m gonna put the hammer down!”
We were sailin’ through interstellar space about 90 times the speed of light,
we met a cave full of Klingon Smokey Bears, and we passed 'em on the right.
They said “Hold on, Federation Roger Ramjet, the limit here’s Factor 3!”
I said “Uhura, did you hear Smokey ask if he could open a hailin’ frequency?”
‘Cause we got ourselves a Star Fleet, trekkin’ through the night.
Yes, we got ourselves a Star Fleet, ain’t she a beautiful sight?
Come on and join our Star Fleet, ain’t nothin’ gonna get in our way!
We’re gonna take our mighty Star Fleet across the Milky Way!
Star Fleet!
Star Fleet!
Wow, I know I’ve never heard that, because I’d have remembered! Sounds clever.
Here’s a palate cleanser between Google searches…
A fellow member of the SCA wrote it down for me at the party following a tournament. I carried the notebook around with me for about six months and then lost it. 
And that was … vintage Shatner! 
I haven’t listened to @Elmer_J.Fudd ’s ‘Shatner singing Convoy’ link yet, but I totally read this in my head using Shatner voice.
The rest of the lyrics I remember are
We were half a parsec front door to back, and a light-year edge to edge,
and we showed them Klingon Smokey Bears how far the Treaty’d stretch.
We had cargo liners, cruisers, scouts; we had dreadnoughts fore and aft,
and 16 long-eared Vulcan hippies in a rented shuttlecraft.
[Pshhht!] Uh, put them Vulcans in behind the cargo liner, his computer’s gone out! [Pshhht!]
[Chorus]
Well, we’d just come out of Klingon space, and what should lie ahead,
but a Romulan border checkpoint, and my phaser banks were dead!
I said “Scotty, this here’s Captain Kirk, I don’t believe I can read that sign!”
So we shot the gate at Warp Factor 8, and we left 'em all behind!
[Chorus]
[Pshhht!] Ah, ten-four, good buddy, keep the matter side in and the anti-matter side out! [Pshhht!]
Maybe it was a thing that only traveled in SCA circles like numerous other of their parody songs.
Could have been. I don’t remember him telling me where it was from, or even if I asked him that.
Wow, I’ve been a C.W. McCall fan since the mid-Seventies, and I thought I’d heard all the parodies. That’s a new one for me!
Similarly (As far as maybe it was just a local thing) at my first convention around 1978, a guy was selling xerox copies of a comic parody of “Where No Man Has Gone Before”
The only joke I remember was “I’ll crush you! Crush you like elephants!”…“Thinks big doesn’t he?”
I assume this was something the guy himself had done. I loved the bootlegness of old old conventions. We saw Trek eps, the TOS bloopers, showings of When The Earth Stood Still. All in rooms about as big as a large living room.
Holy crap check out this program. Masquerade ball at 10pm? Yikes. And “What its like to sleep with a Sci-Fi writer” with Guy Haldeman (Joes wife)
Needless to say, I was just there for a few hours during the day, and missed the drunk Sci-Fi debauchery Im sure went on.
My guess is it’s amateur filk.
Ditto!!
And speaking of C. W. McCall, are you aware that his back-up band for “Convoy” still sort-of exists and performs yet today… as “Mannheim Steamroller”? Yup, Chip Davis had been working as a advertising executive in the Omaha area and created the character of C.W. for a series of bread commercials. He had also formed a ‘New Age’ musical group in 1974 that would eventually become “Mannheim Steamroller”, and tapped several of these original members for the commercials and, later on, the C.W. McCall recordings (where they were credited as “The Fort Calhoun Nuclear Power Plant”).
And if you listen to some of the later C.W. McCall stuff, like “There Won’t Be No Country Music”, “Aurora Borealis”, or “Roses for Mama”, and pay attention to the backing music, you can hear the Mannheim sound starting to gel even back then.
-“BB”-
How are you able to remember all of those lyrics? Did you hear the song over and over? If so, how? Was it played on a local radio station?
Did some not quite famous writer try to drink a bottle of booze sitting on a window ledge, and fall to his death?
I made it a point to memorize them while I still had the notebook in my possession. I remember performing the song once around a campfire at a folk festival on the Isle of Man in June 1976.
As mentioned above, the lyrics were written out for me by someone I’d never met before and whose name I don’t recall. (This was in March 1976.) I have never heard it performed by anyone else, nor have I ever found another person who knows of it. Hence the question asked in my original post.
The size of that convoy was impressive! Must have made staying in formation kind of tough with the radio lag and all. Or did the Star Trek universe solve that problem and allow instant communication.