Pattinson, 28, and 26-year-old Twigs have not commented on their relationship yet but have been spotted together many times in the recent past, reported Aceshowbiz.
The singer took to Twitter to address the issue.
"I am genuinely shocked and disgusted at the amount of racism that has been infecting my account the past week. Racism is unacceptable in the real world and it's unacceptable online," she tweeted.