In most states, no, you aren’t allowed to text at a red light or stop sign. However, there is a legal loophole in certain states.
For instance, in New York and Missouri, texting while the vehicle is stopped is legal; only texting while the vehicle is in motion is banned. However, your foot needs to be on the brake, because if the car even moves an inch while you are texting, it becomes illegal. Be sure to review your most recent state and local laws for specifics.