The singer has said he was inspired to take part in the ITV ice-skating competition by Parker, who died last year aged 33 after battling an inoperable brain tumour.
And at the weekend, he skated to the band's Gold Forever in the semi-final.
Before he took to the ice, Kaneswaran shared a clip on Instagram of The Wanted on stage with Parker in one of his final performances.
"This skate tomorrow is probably one of the most challenging things I’ve had to do in my entire life," Kaneswaran wrote.
"But I know you would do the same for me Tommy boy. This one's for you brother x."
Kaneswaran was emotional in his interview before he skated, saying he wanted everyone to know how "incredible" Parker was and that his skate was in memory of the singer.
He said he wanted everyone to celebrate the late dad-of-two.
Viewers were touched by the poignant tribute and many said they were in tears.
"Just watched Siva’s performance and I can’t stop crying, Tom would be so proud," one person posted on Twitter.
Another said: "Siva's dance was beautiful and the most touching tribute to our late great Tommy P."
"Siva did Tom Parker so proud tonight had me balling," posted another fan.
"What a beautiful song for a beautiful soul."
Another said seeing a picture of Parker flash up during the performance "broke" them.
"In tears the whole way through," they added.
While he wowed viewers and the judges, Kaneswaran did not secure a slot in the Dancing On Ice final, with The Vivienne, Joey Essex and Nile Wilson going through to the last stage.
Parker was diagnosed with inoperable stage-four glioblastoma in 2020.
He documented his battle with his fans on social media and had been determined to beat the odds.
However, in March last year, his wife Kelsey posted a message on Instagram saying that the star had passed away peacefully with his family at his side.
Watch: The Wanted singer Tom Parker posthumously shortlisted for NTA for brain tumour documentary