The writing was added to the base of the memorial in Parliament Square during the Black Lives Matter protest on Sunday.
Video footage showed a small crowd of demonstrators chanting “Churchill was a racist” and “Boris [Johnson] is a racist”.
A smaller group of people stood around the statue in an apparent attempt to protect it.
Four uniformed police stood nearby as the crowd took photographs.
Banners with messages such as “British Colonialism is to Blame” and “What if it was your son?” had earlier been left at the base of the column.
A Black Lives Matter sign was also strapped to Churchills’ belly.
The same statue was targeted by protesters on the anniversary of D-Day on Saturday, when the letters “ACAB” were added to the base in green neon paint. It is believed to stand for “All Cops are B****rds”.
Another sculpture of Churchill in New Bond Street, central London, was splashed with white paint in January 2019.
The latest incident happened shortly after demonstrators in Bristol tore down a statue of 17th slave trader and threw it into the city’s river.
Avon and Somerset launched a police investigation, while home secretary Priti Patel described the incident as “sheer vandalism”.