The 85-year-old singer has been a vocal critic of the commander-in-chief so was thoroughly unimpressed when he shared a video of the legendary crooner singing his most famous song, My Way, on his Truth Social platform over the weekend.
A fan wrote on X: "Omg, @NancySinatra will not be happy about this. Trump goes against everything that Frank stood for. He was a big champion for equality and supported the Civil Rights movement."
She replied: "This is a sacrilege."
Nancy voiced her frustration that she was unable to do anything about Trump sharing the video.
Asked by a social media user if she could get it taken down, she replied: "Unfortunately no. The only people who can do something are the publishers."
She also reposted a fan's tweet that read: "Trump may love Sinatra, but Sinatra did not love Trump."
Nancy previously insisted her father - who died in 1998 aged 82 - loathed the former Apprentice star.
In December, she commented on a video of ICE officers confronting construction workers.
She wrote: "This is not my father's America. He would be devastated. Trump is so wrong in so many ways."
Someone then replied: "Your Dad would have loved Trump."
But Nancy hit back: "Do some homework before you make a fool of yourself. My dad LOATHED Trump."
A host of musicians have previously complained about Trump using their music including Johnny Marr, The Rolling Stones and the Village People, as well as the estates of the late Sinead O'Connor and Tom Petty.