She said he started making threats to other passengers, but the flight crew and passengers "handled it so well".
After the "drunk and belligerent" passenger was removed, she wrote, "God bless him, he thought the cops were his "car service" and asked them to make sure his luggage got to his house".
Another Twitter user, Rebecca Shepard wrote, "Crazy dude on my plane to San Diego from Boston. @AlaskaAir flight attendants handling so professionally."
The incident meant travellers were subjected to a delay of nearly an hour before the plane and its 181 passengers could resume its journey.
An Alaska Airlines spokesman told NBC News the man "was told to calm down by flight crew, and then became agitated and verbally abusive, even issuing a threat to flight crew".
"Out of an abundance of caution, the captain decided to land at the nearest airport, which was Denver International Airport," he said.
"The plane landed safely and taxied to the gate where Denver Airport police met the plane and took the passenger into custody."
The incident follows a similar example of bad behaviour high in the skies.
Earlier in the week a shirtless man was removed from an Air Mediterranee flight from Algeria to Paris after he urinated on a fellow passenger.
- nzherald.co.nz