The Live and Let Die star was first introduced to the late British royal at a film premiere, but admits he felt guilty chatting to her after downing whiskey.
He tells Britain's Ok! magazine, "We met at a premiere and I was stinking of Jack Daniel's. I was worried I'd breathe my alcoholic breath all over her. And she was such a virgin. At that time! I thought she'd fall over with one whiff of my breath!"
Sir Roger, who was knighted in 2003, insists he has a special place in his heart for another royal - monarch Queen Elizabeth Ii.
He adds, "I've met them all, but my favourite is the Queen. If you're English and you've been brought up to have tremendous respect for the Queen then it is awe-inspiring. It's surreal. I was very nervous."