The Angels hitmaker took to Instagram on Wednesday evening, where he shared the sweet clip.
It showed Robbie having his makeup done as he sat back on a plush sofa.
His two-year-old stood in front of him with her back to the camera, wearing a loose white top and blue and white bird print leggings.
The singer encouraged his daughter to sing Shake it Off with him by asking her, "And the haters gonna…" to which the little girl replied: "Hate hate hate."
WATCH: Robbie Williams melts fans' hearts with video of daughter Coco singing
Robbie then prompted Coco: "And the players gonna…" His daughter deviated a little from the song at this point in the most adorable way, emphatically singing: "Shut up!"
The pair then sang the same lyrics again, and Robbie pulled Coco onto his knee to finish their sweet performance. The star captioned the post: "What do you think @taylorswift."
There's been no word from the American superstar, but the former Take That member's fans were quick to comment on how impressed and touched they were.
Many posted hearts and clapping emojis, and one commented: "Omg melts my heart, love seeing you be [a] daddy, too adorable."
Robbie is a doting dad to his four children
A second gushed: "Adorable, have been a fan of you from the very beginning, now I'm a fan of your family."
Others wrote: "Cuteness overload," and: "Love this! My little lady loves Shake It Off too!"
The happy couple are devoted parents to two sons: Charlie, five, and Beau, who was born in February.
They share two daughters, Coco and Teddy, eight, who is also musical, being a keen piano player.
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