The Dundee-born star spoke out following David Bowie's call for Scotland to remain part of the UK at the Brit Awards last month.
Cox, who splits his time between Scotland and the US, told e-magazine Boo York City: 'I think Americans ought to be pro-independence. You just need to say to them "Why did your forebears go to the States? They went for a better life.
'These people wanted to have equality. And Scots haven't had that - we've grown up with a sense of inferiority so that when we go to America we immediately discuss how positive everyone is.'
Cox, whose credits include Braveheart, Manhunter, and Rob Roy, and has starred in the first two episodes of the BBC TV series Shetland, feels that the UK government is trying to obfuscate the independence issue by threatening to take away the pound if Scotland becomes independent.
He says in the article: 'This whole argument has nothing to do with the pound. It's not about any of these things they say are important; it's about .....and trying to get back to egalitarian principles, which is so present in the Scottish character.
'Another problem England has is that the parliament is in London and it shouldn't be. London is London - it's a separate principality, which has nothing to do with England. Absolutely nothing. London is a different state, and it always has been. It's like Monaco…or Lichtenstein.
'The playwright David Hare was talking in the press about how he was happy for Scotland to vote 'Yes' because he thought that would finally shed light on what was lacking in the democracy of England, and I think he's hit the proverbial very firmly on the head.
'The democratic position of the so-called United Kingdom over the last 50 years has suffered, like the very shores of the islands themselves, from a process of systematic erosion.
Cox, who is to receive a Lifetime Achievement Award from Bradford International Film Festival next month, says: 'The United States appeals to Scots. Though it certainly has its problems with its moneyed class, at grassroots it's egalitarian and Americans have that principle written in to their constitution.'
A spokesmann for First Minister Alex Salmond told the magazine: 'We're delighted that such a distinguished and high-profile actor as Brian Cox is highlighting the campaign for Scottish independence stateside.
'Although he won't have a vote - as the decision is quite rightly a matter for the people who choose to live and work in Scotland - Brian is a powerful voice and makes a welcome contribution to the debate.
'The world is watching Scotland as we approach the historic referendum, and vocal campaigners like Brian are big factor in the steady increase in support for a Yes vote that we have seen over the last few months. Most people would agree that independence has worked out well for the US, so Brian's appeal will definitely be well-received.'