The 26-year-old singer - whose real name is Tahliah Barnett - has taken to her Twitter account to claim she has been inundated with horrific comments in the past week after confirming her relationship with the 28-year-old hunk.
She wrote: ''I am genuinely shocked and disgusted at the amount of racism that has been infecting my account the past week.''
The star added: ''Racism is unacceptable in the real world and it's unacceptable online.''
Last week, Robert was said to have ''fallen hard'' for his new girlfriend following his split from Kristen Stewart, his girlfriend of five years.
A source said: ''Rob is falling hard for Tahliah. He's just enamoured with her beauty, creativity and confidence. He hasn't felt this way about someone since Kristen.
''This is his girl and Rob is beyond proud to show her off. They became instant friends at first and it blossomed into a romance. He's really taken with her and not afraid to show it.''
FKA previously revealed she suffered racist abuse when she was younger as the only mixed-race girl in a Catholic school.
She recently told Dazed and Confused magazine: ''Either your hair's different, or the colour of your skin, or your features. Half of my life I've had people staring at me because they think I'm funny-looking and ugly.''
We explore the musical culture of Camden as Madness and Amy Winehouse receive their stones on the Music Walk of Fame.
The Quarterhouse, and Melting Vinyl, played host to two inspired performances in Folkestone on the first evening of March.