First, Hopkins' himself does not identify as a Method actor. However, what he does is fairly consistent with the Method anyway. Under the Wikipedia entry on Method Acting, we read:
Method acting, known informally as the Method, is a range of training and rehearsal techniques, as formulated by a number of different theatre practitioners, that seeks to encourage sincere and expressive performances through identifying with, understanding, and experiencing a character's inner motivation and emotions. These techniques are built on Stanislavski's system, developed by the Russian actor and director Konstantin Stanislavski and captured in his books An Actor Prepares, Building a Character, and Creating a Role. links removed
Anthony Hopkins is considered a "Classically Trained" actor, and is known for theater (stage) as much as films. He is among those recognized as a Shakespearian thespian. To memorize Shakespeare and perform it on stage, well, is an accomplishment. I know many high school drama departments do Romeo and Juliet, for example, but watching a high school performance and comparing it to a well done play by classically trained actors is amazing.
To get back on track, however, it has been said:
While Hopkins doesn’t identify himself as a method actor, he does think his approach of deep-learning his lines has an affect on his mental performance. He says, “Well, I learn the text so deeply that I think it has some chemical effect in my brain. I’ve been playing some pretty tough guys, like King Lear, or this guy with dementia in The Father. It’s exhausting, but I’m not a method actor in that sense. I believe in learning the text which is there. Once you know it so well that you can improvise and make it real, it’s easy. You can’t pretend to know it – it’s impossible to, and I couldn’t do it. I’ve worked with actors who don’t know their stuff, and they were just wasting everyone’s time.”
With that said, Hopkins does think of himself as an actor who can easily be scary on screen. He explains, “Oh yes, I know I can. It’s a technique. When I read the script of The Silence of The Lambs I thought, ‘Ah, I know how to play this guy.’ You get a sense of how you could do it: the more subtle and quiet you are, the scarier it is.”
However, in another interview, he said:
“When I tell people that I just learn my lines and that’s all there is to it, my wife thinks that I’m putting down the craft of acting,” the 69-year-old actor explained in his suite at the Four Seasons Hotel in Los Angeles.
“But I’m not putting it down. I have nothing but respect for the craft. And I could come up with all sorts of fancy theories about playing these characters but, basically, it’s just a matter of learning the lines. I’m sure that Robert De Niro and all the other Method guys would not approve of that.
“I admire them, but I’m just as Method as those guys. But I believe that the text is all the information you need.”
So, he does agree that his style is kind of Method, but he just wasn't trained in the Method formally.
Whatever method (pun intended) Hopkins' uses, it works. In the words of his co-star from The Silence of the Lambs, Jodie Foster:
During her appearance on The Graham Norton Show, host Graham Norton asked Jodie Foster about is it true that she never spoke to Anthony Hopkins while shooting the film. Answering this, Jodie Foster replied by saying, “No. Never spoke to him. He was scary.” She further mentioned that on the first day, they had a read through where everybody was sitting down and they had a read-through of the movie. She revealed by the end of the reading, she never wanted to talk to Anthony Hopkins again as she was petrified.
Talking about the filming experience, Jodie Foster shared that Anthony Hopkins was always behind the glass partitions or he was in his cell. As the scenes were long, Anthony Hopkins was locked inside at the beginning of the day and on the next day he used to be on the other side and she would be on the opposite side. This is how they got to the end of the film and never actually had a conversation as such, revealed the actor. Jodie Foster also said that she used to really avoid him.
It is telling that an actor of Jodie Foster's caliber (she had been acting, off and on for 23 years, starting at age 3) that she was "scared of Hopkins" ... in other words, he was so well in character that she could play off his abilities.
Finally, you mention The Actor's Studio. According to its website:
"The Actors Studio, founded in 1947, was created and survives today as a unique theatre workshop where members gather together to work on their craft in private.
Through moderated sessions, workshops, and readings, the Studio offers its members – free of charge – a dynamic, creative atmosphere, as well as a safe haven away from commercial pressures. The Actors Studio helps professional actors, directors, and playwrights hone their craft and explore the depth and breadth of their talent.
Based on exercises and techniques developed here by Lee Strasberg and others, The Actors Studio is ‘the home of method acting.’"
You should be aware that The Actor's Studio had Anthony Hopkins in their televised program "Inside The Actor's Studio".
That television program was: "The program began as a televised craft seminar for students of the Actors Studio Drama School, originally a joint venture of the Actors Studio and New School University in 1994, with Paul Newman, a former Actors Studio president, as its first guest, and soon became Bravo's flagship program." So the fact that in a Nationally televised seminar they actually had Anthony Hopkins as a guest to explain his craft to their students, and us viewers, shows that they thought highly of his abilities, in the method of the Method.
EDIT: As Tetsujin also says, as I was writing this, I knew someone else posted an answer, but didn't know what it was. I bow to his expertise, being a working actor himself, and one who has had the opportunity to actually work with Mr. Hopkins.