However, the Harry Potter star also said he could understand why some Scots would want independence and said it was fair the decision was taken north of the border.
Radcliffe's comments came at an event in New York, organised by the online news aggregator, Buzzfeed.
He said: "I personally like the UK being how it is but I can totally see why some people in Scotland might want independence.
"But it's not up to me; I don't get a say in the future of Scotland and that's fair. I'm sure they'll make the right decision for their country."
Earlier this month JK Rowling, author of the Harry Potter books, gave her backing to Better Together and donated £1m to the pro-union campaign.
Rowling received abuse on Twitter and Radcliffe said similar incidents were enough to put him off social media.
"It is just a whole lot of craziness. Twitter is brilliant for some things...but for me I am not that concise anyway so I wouldn't do that well out of it as a format."