Light painting is a photography technique of capturing a light moving when the camera shutter is open making it a long exposure shot. There are different methods to light paint; keeping the camera stable and keeping the shutter open in front of moving lights (could be traffic), or using a torch, led lights, etc. to draw patterns and more.
Your mobile phone native camera may not allow you to manually control the shutter to get long exposure images. It can be achieved by third-party apps which gives you more control over your camera.
Make sure you fix your mobile phone to a tripod or keep it stable because the app will need some time to finish taking the photo until you are doing with the light painting.
Jason D. Page has made a video of how he light paints Stay Home using the slow shutter app. He shows a technique where he sits and writes it using the light he has which is from Light Painting Brushes. He also shows how to write using light against a backdrop.