The Troy star confessed to smoking the morphine-based substance when he visited an opium den in Mumbai during a theatrical tour of the country in the 1980s.
Cox admits he only tried it once as an experiment but insists the drug gave him a feeling of being "very at one with the world".
He tells Scottish newspaper The Herald, "It's something I have spoken about privately but never before in such a public way. I believe you have to be honest and admit your humanity. You can't be above it all.
"When I went to India, I was in an environment when I could try it in the right conditions. It was the conditions that were important. It was only there I could try it - so I did.
"I tried other things. In Calcutta I had bhang lassi, a yoghurt drink with poppy seeds at the bottom which has a slightly hallucinogenic effect.
"I have no regrets, but I do think you have to be responsible. I was never into it when I was younger because I didn't like the idea of it. I was very puritanical. I thought it was a bit of an indulgence on people's parts."
Cox reveals his drug-dabbling as part of a TV documentary series for BBC Scotland.