The actor appeared to forget the name of his "Two Lovers" co-star, Gwyneth Paltrow, stuck gum under the edge of Letterman's "Late Show" desk and appeared to curse at bandleader Paul Shaffer for laughing at him during Wednesday night's show.
Clips of the sunglass-wearing Phoenix's appearance were racing around the Internet on Thursday.
"I'm sorry you couldn't be here tonight," Letterman said after his interview, punctuated by intervals of uncomfortable silence from both.
Phoenix, a two-time Academy Award nominee, now sports a long, black beard and announced last October that he was quitting acting to concentrate on a career as a hip-hop musician. He has said that "Two Lovers," a romantic drama, is his last movie. It's such an odd career switch that some are wondering if it's all an act, particularly since Casey Affleck was following Phoenix with a camera to film him at the "Late Show." Phoenix has insisted it isn't.
Letterman drew immediate attention to Phoenix's appearance when the actor sat down for his interview.
"I will just say right off the top here, you look different than I remember you," the talk show host said. When he asked, "How is the beard?" and the audience laughed, Phoenix mumbled something about being made to feel weird about his appearance.
Phoenix appeared on the show to promote his movie. Letterman asked about Paltrow and momentarily forgot her name. Phoenix couldn't, or wouldn't, help him. Following a few seconds of uncomfortable silence, Letterman said, "Can you tell us about your days with the Unabomber?" Phoenix didn't reply, but allowed the slightest hint of a smile at the joke.
They talked about Phoenix's decision to quit acting. When Letterman asked why, Phoenix replied, "I don't know."
"Here's my hope, after a little time off - and I think you're taking a little time off tonight - I'm hopeful you will reconsider and come back to acting because there's nobody really better than you are," Letterman said.
Letterman veered between mocking Phoenix and trying with little success to draw something out of him. When Letterman asked if Phoenix had fun working with Isabella Rossellini, he said, "Yes," but was silent when questioned whether he had any stories to tell. "I'm sure something fun happened," Phoenix said.
Phoenix's desire to be a hip-hop musician was met with little enthusiasm from Letterman. "I'd love to come on the show and perform," Phoenix said.
"You know, that seems unlikely," Letterman said. "We'll certainly keep you in our Rolodex." The audience laughed and Phoenix said nothing.
Letterman asked Phoenix to introduce a clip from "Two Lovers," which seemed so unlikely given how the interview was going that Shaffer guffawed.
Phoenix turned to Shaffer, asking "are you ... serious," with a word bleeped out. He wondered aloud why the audience was laughing at him. "What do you have them on? Is this nitrous?" Phoenix said.
And when Letterman noted that the actor was chewing gum during his interview, Phoenix took the wad from his mouth and stuck it under the lip of Letterman's desk.
The general weirdness made viewers - and Letterman - recall Farrah Fawcett's memorably spacey "Late Show" appearance in 1997. "We owe an apology to Farrah Fawcett," Letterman said at the interview's end. In Fawcett's appearance, the giggly, distracted actress talked about using her body parts to paint pictures and briefly thought Letterman's stage backdrop of a New York City skyline was real.
A spokeswoman for Phoenix did not immediately return a call for comment on Thursday.
Phoenix, in a recent interview with The Associated Press, said that he grew his beard as a way of distancing himself musically with his best-known acting role, Johnny Cash, in the 2005 movie "Walk the Line." He acknowledged that his career change looked odd but said he is utterly serious about it.
"I have better things to do than just, like, (mess) around with people," he said. "This is my life and this is my work, and this is the thing that I've been passionate about. Just because it's hard for other people to recognize and to see that, look, I get it, dude. I know that it seems ... weird. ... But I can't let that affect my life and the things that I want to do."
The 34-year-old star received Oscar nominations for his roles in "Gladiator" and "Walk the Line," for which he learned to play guitar to channel country legend Johnny Cash.
AP Movie Writer David Germain contributed to this report.
By David Bauder