So far the answer seems to be Goon Show.
Which just goes to show, the answer to everything is always Spike Milligan.
A more recent contender than the Goon Show, although it’s not for comedic effect, but does serve as punctuation of sorts:
In “Dirty Dancing (1987),” Patrick Swayze drags the needle just before Neal (Neil?) tells him that he wants him to do. . . The Pechanga!.
Living Doll with Cliff Richard & The Young Ones (1986) ends with one of these, cutting Rick off before he can utter an expletive.
It was indeed used in “Weird Science,” when Lisa and the boys first walk into the Kandy Bar.
Another cite: “Trading Places” (1983). Eddie Murphy does a record scratch just before he throws his party-goers out of his new digs.
Edit: Whoa! Ten years since the last post?
Pretty sure it was used on The Goon Show, which was a pre-Monty Python British radio comedy show [airing 1951-1960]. Sound effects were always a big part of the humour and both parodied normal noises and subverted expectations. There were many scenes where a cliche version of one of our heroes walking into a noisy bar would be interrupted with a record scratch and silence would fit the story.
Sorry, cannot be more precise or quote a specific show.
Tvtropes, which is not intended to be a historical record, mentions that Stan Freberg used the sound effect in his short-lived 1957 radio show.
Between that and The Goon Show, we’re somewhere in the 1950s. Can anyone go further back?