Peter Bywaters, of Peter & The Test Tube Babies, claims he was detained when he flew in for a festival.
He said he was interrogated for six hours by border control staff and shown photos of himself dressed up as Donald Trump on tour in Germany last year.
However, US Customs and Border Protection officials say he was deported for having the wrong visa.
In a statement to EW, spokesman Jaime Ruiz said: "The claim that he was refused entry to the United States because he mocked the president of the United States, that is absolutely not true.
"That is false. The reason he was denied entry was because he came with the wrong visa."
After being questioned by customs and border staff in San Francisco, Peter Bywaters says he had his phone and passport confiscated, had a DNA swab taken, was photographed and had to make an official statement before being escorted to a plane bound for London.
He told the website Team Rock: "I had only been there 30 seconds when the border control guard swung his screen round and said, 'Is this you?'
"There in full view was a video from last year's German tour with me dressed as Donald Trump smoking a fake joint.
"From there it all went downhill. Six hours later I was forcibly escorted to my seat on the plane."
He was refused alcohol on the 11-hour United Airlines flight back to the UK and only had his mobile and passport returned when he'd landed.
"I expect to still be the singer of Peter & The Test Tube Babies by the end of the year," he said.
"Will Trump still be president by the end of the summer? A US tour or festival will never, ever happen again."
The rest of Peter & The Test Tube Babies performed at the Punk Invasion Festival in Orange County, California, with the help of several guest singers on Saturday - including Joey Bondage from Narcoleptic Youth, Ron Conflict from Lower Class Brats, Gabe Zander from Oi Scouts and Mike Blank from Blank 77.
The band, who formed in 1978 in East Sussex, release their new album in September.