The actor said Scotland "has the ability" but needs more studio space to be able to capitalise on its talent.
Plans to create a full-time permanent film studio in Scotland - in addition to the converted warehouse in Cumbernauld where the Outlander TV series is shot - have been troubled.
A £250 million purpose-built facility planned for the Pentland Estate on the outskirts of Edinburgh was stymied last year by a court ruling in a land tenancy row, prompting a change of plans to a site at Dalkeith, Midlothian.
Separately, Screen Scotland planned to put a private firm in place to turn a former wave power plant at the city's Leith Docks, used in producing Marvel's Avengers: Infinity War, into a round-the-clock film studio last spring but this deadline was missed.
Now, Cox - who won best actor in a TV drama for his role as ageing media magnate Logan Roy in Succession at the Golden Globe awards in LA on Monday - wants more to be done.
Speaking on BBC Scotland's The Nine, he said: "We've got great crews in Scotland - that's why we really need to get that studio off the ground.
"We can service so many films, we've got the ability. I've done two or three in Scotland.
"So I know the props guys, the film workers in Scotland are pretty phenomenal, and I want to see more work happening."
Parts of Succession were filmed in the Dundee native's home city, including in the new V&A museum, and he said "I think everyone was delighted to be in Dundee."
Cox, 73, whose film roles include Manhunter, The Bourne Identity and Troy, spoke of his reaction to being named a Golden Globe winner.
He said: "It was extraordinary - it does your head in at these kind of events.
"You are always happy when it gets announced, either when you lose or when you win it.
"I actually apologised to my fellow nominees because it's such hell that you go through for that 30 seconds. But it was wonderful."