"Volpla", a novelette by Wyman Guin; first published in Galaxy Science Fiction, May 1956 which is available at the Internet Archive, as is the X Minus One radio adaptation; the story is also available at Project Gutenberg. Any of these covers look familiar?
He started with rats:
The fact was that I had something more in the lab than I had bargained for. I had aimed only at a gliding mammal a little more efficient than the Dusky Glider of Australia, a marsupial. Even in the basically mutating colony, there had been a decidedly simian appearance in recent years, a long shift from the garbage-dump rats I had started with. But my first volplas were shockingly humanoid.
There were also much faster than had been their predecessors in organizing their nervous activity after the slumbering explosion of growth in the metabolic accelerator. When I returned to the lab, they were already moving about on the mattress and the mail was trying to stand.
He created them as a joke:
I sipped at my martini and lounged in a terrace chair watching the golden evening slant across the beautiful hills of our ranch. I dreamed. I would invent a euphonious set of words to match the Basic English vocabulary and teach it to them as their language. They would have their own crafts and live in small tree houses.
I would teach them legends: that they had come from the stars, that they had subsequently watched the first red men and then the first white men enter these hills.
When they were able to take care of themselves, I would turn them loose. There would be volpla colonies all up and down the Coast before anyone suspected. One day, somebody would see a volpla. The newspapers would laugh.
Then someone authoritative would find a colony and observe them. He would conclude: "I am convinced that they have a language and speak it intelligently."
The government would issue denials. Reporters would "expose the truth" and ask, "Where have these aliens come from?" The government would reluctantly admit the facts. Linguists would observe at close quarters and learn the simple volpla language. Then would come the legends.
Volpla wisdom would become a cult—and of all forms of comedy, cults, I think, are the funniest.
He gives them their legends:
"The old ones told me you came long before the red men in a ship from the stars." Standing there in the dark, I had to grin, visioning the Sunday supplements that would be written in a year, maybe even less.
He looked into the sky for a long time. "Those little lights are the stars?"
I glanced about and presently pointed over a tree. "From Venus." Then I realized I had blundered by passing him an English name. "In your language, Pohtah."
They take off in a commandeered rocket to Venus:
For a moment there was only a gritty buzz from the receiver. Then the tape started playing a soft, high voice. "This is Rocket Harold saying everything is well. This is Rocket Harold saying good-by to men." There was a pause and then, in clear volpla language, another voice spoke. "Man who made us, we forgive you. We know we did not come from the stars, but we go there. I, chief, give you welcome to visit. Good-by."