A group of Donald Trump supporters emblazoned their delight at his inauguration across the Sydney skyline on Saturday, paying a skywriting company to write the new President's name among the clouds.

The letters T-R-U-M-P appeared in the sky just as thousands of women took to the CBD streets to protest against the Trump presidency.

Pilot Rob Vance etched out the new President's name twice from 12.30pm. He said those who commissioned the stunt wished to remain anonymous as they feared a backlash.

"They were Trump supporters," Mr Vance, of Skywriting Australia, said. "I can tell you that.